---
OA_place: publisher
OA_type: hybrid
_id: '21379'
abstract:
- lang: eng
text: We study a (1 + 1)-dimensional semi-discrete random variational problem that
can be interpreted as the geometrically linearized version of the critical 2-dimensional
random field Ising model. The scaling of the correlation length of the latter
was recently characterized in Probab. Duke Math. J. 172(9), 1781–1811 (2023) and
arXiv:2011.08768v3, (2022); our analysis is reminiscent of the multi-scale approach
of the latter work and of Combinatorica 9, 161–187 (1989) . We show that at every
dyadic scale from the system size down to the lattice spacing the minimizer contains
at most order-one Dirichlet energy per unit length. We also establish a quenched
homogenization result in the sense that the leading order of the minimal energy
becomes deterministic as the ratio system size / lattice spacing diverges. To
this purpose we adapt arguments from arXiv:2401.06768, (2024) on the (d + 1)-dimensional
version our the model, with a Brownian replacing the white noise potential, to
obtain the initial large-scale bounds. Based on our estimate of the (p = 3)-Dirichlet
energy, we give an informal justification of the geometric linearization. Our
bounds, which are oblivious to the microscopic cut-off scale provided by the lattice
spacing, yield tightness of the law of minimizers in the space of continuous functions
as the lattice spacing is sent to zero.
acknowledgement: FO and CW thank Ron Peled for insightful discussions on the white-noise
multi-dimensional case in the Fall of 2023. CW thanks Barbara Dembin for the discussion
during a workshop in Spring 2025. The work was done while the authors were affiliated
with the Max Planck Institute for Mathematics in the Sciences; CW thanks the MPI
for the support and warm hospitality. Open access funding provided by Institute
of Science and Technology (IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Felix
full_name: Otto, Felix
last_name: Otto
- first_name: Matteo
full_name: Palmieri, Matteo
last_name: Palmieri
- first_name: Christian
full_name: Wagner, Christian
id: bf0c729b-2619-11f0-8024-9d69bb2b8b20
last_name: Wagner
citation:
ama: Otto F, Palmieri M, Wagner C. On minimizing curves in a Brownian potential.
Probability Theory and Related Fields. 2026. doi:10.1007/s00440-026-01468-y
apa: Otto, F., Palmieri, M., & Wagner, C. (2026). On minimizing curves in a
Brownian potential. Probability Theory and Related Fields. Springer Nature.
https://doi.org/10.1007/s00440-026-01468-y
chicago: Otto, Felix, Matteo Palmieri, and Christian Wagner. “On Minimizing Curves
in a Brownian Potential.” Probability Theory and Related Fields. Springer
Nature, 2026. https://doi.org/10.1007/s00440-026-01468-y.
ieee: F. Otto, M. Palmieri, and C. Wagner, “On minimizing curves in a Brownian potential,”
Probability Theory and Related Fields. Springer Nature, 2026.
ista: Otto F, Palmieri M, Wagner C. 2026. On minimizing curves in a Brownian potential.
Probability Theory and Related Fields.
mla: Otto, Felix, et al. “On Minimizing Curves in a Brownian Potential.” Probability
Theory and Related Fields, Springer Nature, 2026, doi:10.1007/s00440-026-01468-y.
short: F. Otto, M. Palmieri, C. Wagner, Probability Theory and Related Fields (2026).
corr_author: '1'
date_created: 2026-03-02T10:05:23Z
date_published: 2026-02-14T00:00:00Z
date_updated: 2026-03-02T15:15:13Z
day: '14'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00440-026-01468-y
fulldoi: https://doi.org/10.1007/s00440-026-01468-y
has_accepted_license: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.1007/s00440-026-01468-y
month: '02'
oa: 1
oa_version: Published Version
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- 1432-2064
issn:
- 0178-8051
publication_status: epub_ahead
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: On minimizing curves in a Brownian potential
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2026'
...
---
APC_amount: 1352,08 EUR
OA_place: publisher
OA_type: hybrid
PlanS_conform: '1'
_id: '21894'
abstract:
- lang: eng
text: "The Dean–Kawasaki equation—one of the most fundamental SPDEs of\r\nfluctuating
hydrodynamics—has been proposed as a model for density fluctuations in weakly
interacting particle systems. In its original form, it is highly\r\nsingular and
fails to be renormalizable, even by approaches such as regularity structures and
paracontrolled distributions, hindering mathematical approaches to its rigorous
justification. It has been understood recently that it is\r\nnatural to introduce
a suitable regularization, for example, by applying a formal spatial discretization
or by truncating high-frequency noise: This yields\r\nwell-posed equations that
should still precisely approximate the law of the\r\nparticle density fluctuations.\r\nIn
the present work, we prove that a regularization in the form of a formal\r\ndiscretization
of the Dean–Kawasaki equation indeed accurately describes\r\ndensity fluctuations
in systems of weakly interacting diffusing particles: We\r\nshow that, in suitable
weak metrics, the law of fluctuations as predicted by\r\nthe discretized Dean–Kawasaki
SPDE approximates the law of fluctuations\r\nof the original particle system,
up to an error that is of arbitrarily high order in\r\nthe inverse particle number
and a discretization error. In particular, the Dean–\r\nKawasaki equation provides
a means for efficient and accurate simulations of\r\ndensity fluctuations in weakly
interacting particle systems."
acknowledgement: All authors gratefully acknowledge funding from the Austrian Science
Fund (FWF) through the project F65. CR gratefully acknowledges support from the
Austrian Science Fund (FWF), grants P30000, P33010, W1245. FC gratefully acknowledges
funding from the European Union’s Horizon 2020 research and innovation programme
under the Marie Skłodowska-Curie grant agreement No. 754411.
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Federico
full_name: Cornalba, Federico
last_name: Cornalba
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Jonas
full_name: Ingmanns, Jonas
id: 71523d30-15b2-11ec-abd3-f80aa909d6b0
last_name: Ingmanns
orcid: 0009-0008-1310-7946
- first_name: Claudia
full_name: Raithel, Claudia
last_name: Raithel
citation:
ama: Cornalba F, Fischer JL, Ingmanns J, Raithel C. Density fluctuations in weakly
interacting particle systems via the Dean–Kawasaki equation. The Annals of
Probability. 2026;54(1):155-215. doi:10.1214/25-aop1763
apa: Cornalba, F., Fischer, J. L., Ingmanns, J., & Raithel, C. (2026). Density
fluctuations in weakly interacting particle systems via the Dean–Kawasaki equation.
The Annals of Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/25-aop1763
chicago: Cornalba, Federico, Julian L Fischer, Jonas Ingmanns, and Claudia Raithel.
“Density Fluctuations in Weakly Interacting Particle Systems via the Dean–Kawasaki
Equation.” The Annals of Probability. Institute of Mathematical Statistics,
2026. https://doi.org/10.1214/25-aop1763.
ieee: F. Cornalba, J. L. Fischer, J. Ingmanns, and C. Raithel, “Density fluctuations
in weakly interacting particle systems via the Dean–Kawasaki equation,” The
Annals of Probability, vol. 54, no. 1. Institute of Mathematical Statistics,
pp. 155–215, 2026.
ista: Cornalba F, Fischer JL, Ingmanns J, Raithel C. 2026. Density fluctuations
in weakly interacting particle systems via the Dean–Kawasaki equation. The Annals
of Probability. 54(1), 155–215.
mla: Cornalba, Federico, et al. “Density Fluctuations in Weakly Interacting Particle
Systems via the Dean–Kawasaki Equation.” The Annals of Probability, vol.
54, no. 1, Institute of Mathematical Statistics, 2026, pp. 155–215, doi:10.1214/25-aop1763.
short: F. Cornalba, J.L. Fischer, J. Ingmanns, C. Raithel, The Annals of Probability
54 (2026) 155–215.
corr_author: '1'
date_created: 2026-05-20T08:25:25Z
date_published: 2026-01-01T00:00:00Z
date_updated: 2026-05-21T07:21:25Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1214/25-aop1763
ec_funded: 1
external_id:
arxiv:
- '2303.00429'
file:
- access_level: open_access
checksum: 3e60c0e25a1c96342029a7d2b031505f
content_type: application/pdf
creator: dernst
date_created: 2026-05-21T07:11:27Z
date_updated: 2026-05-21T07:11:27Z
file_id: '21906'
file_name: 2026_AnnalsProbability_Cornalba.pdf
file_size: 865745
relation: main_file
success: 1
file_date_updated: 2026-05-21T07:11:27Z
fulldoi: https://doi.org/10.1214/25-aop1763
has_accepted_license: '1'
intvolume: ' 54'
issue: '1'
keyword:
- Weakly interacting particle systems
- fluctuating hydrodynamics
- Dean-Kawasaki equation
- stochastic PDEs
- numerical approximation
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 155-215
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: The Annals of Probability
publication_identifier:
eissn:
- 2168-894X
issn:
- 0091-1798
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Density fluctuations in weakly interacting particle systems via the Dean–Kawasaki
equation
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 54
year: '2026'
...
---
OA_place: repository
OA_type: green
_id: '22718'
abstract:
- lang: eng
text: Both Newtonian and non-Newtonian fluids may exhibit complex slip behaviour
at the boundary. We examine a broad class of slip boundary conditions that generalises
the commonly used Navier slip, perfect slip, stick-slip and Tresca friction boundary
conditions. In particular, set-valued, nonmonotone, noncoercive and dynamic relations
may occur. For a unifying framework of such relations, we present a fully discrete
numerical scheme for the time-dependent Navier–Stokes equations subject to impermeability
and general slip-type boundary conditions on polyhedral domains. Based on compactness
arguments, we prove convergence of subsequences, finally ensuring the existence
of a weak solution. The numerical scheme uses a general inf-sup stable pair of
finite element spaces for the velocity and pressure, a regularisation approach
for the implicit slip boundary condition and, most importantly, a general Nitsche
method to impose the impermeability and a backward Euler time stepping. One of
the key tools in the convergence proof is an inhomogeneous Korn inequality that
includes a normal trace term.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Pablo Alexei
full_name: Gazca-Orozco, Pablo Alexei
last_name: Gazca-Orozco
- first_name: Franz
full_name: Gmeineder, Franz
last_name: Gmeineder
- first_name: Erika
full_name: Maringová, Erika
id: dbabca31-66eb-11eb-963a-fb9c22c880b4
last_name: Maringová
- first_name: Tabea
full_name: Tscherpel, Tabea
last_name: Tscherpel
citation:
ama: Gazca-Orozco PA, Gmeineder F, Maringová E, Tscherpel T. A Nitsche method for
incompressible fluids with general dynamic boundary conditions. Mathematical
Models and Methods in Applied Sciences. 2026. doi:10.1142/S0218202526500508
apa: Gazca-Orozco, P. A., Gmeineder, F., Maringová, E., & Tscherpel, T. (2026).
A Nitsche method for incompressible fluids with general dynamic boundary conditions.
Mathematical Models and Methods in Applied Sciences. World Scientific Publishing.
https://doi.org/10.1142/S0218202526500508
chicago: Gazca-Orozco, Pablo Alexei, Franz Gmeineder, Erika Maringová, and Tabea
Tscherpel. “A Nitsche Method for Incompressible Fluids with General Dynamic Boundary
Conditions.” Mathematical Models and Methods in Applied Sciences. World
Scientific Publishing, 2026. https://doi.org/10.1142/S0218202526500508.
ieee: P. A. Gazca-Orozco, F. Gmeineder, E. Maringová, and T. Tscherpel, “A Nitsche
method for incompressible fluids with general dynamic boundary conditions,” Mathematical
Models and Methods in Applied Sciences. World Scientific Publishing, 2026.
ista: Gazca-Orozco PA, Gmeineder F, Maringová E, Tscherpel T. 2026. A Nitsche method
for incompressible fluids with general dynamic boundary conditions. Mathematical
Models and Methods in Applied Sciences.
mla: Gazca-Orozco, Pablo Alexei, et al. “A Nitsche Method for Incompressible Fluids
with General Dynamic Boundary Conditions.” Mathematical Models and Methods
in Applied Sciences, World Scientific Publishing, 2026, doi:10.1142/S0218202526500508.
short: P.A. Gazca-Orozco, F. Gmeineder, E. Maringová, T. Tscherpel, Mathematical
Models and Methods in Applied Sciences (2026).
date_created: 2026-08-16T22:01:44Z
date_published: 2026-08-04T00:00:00Z
date_updated: 2026-08-18T07:51:59Z
day: '04'
department:
- _id: JuFi
doi: 10.1142/S0218202526500508
external_id:
arxiv:
- '2502.09550'
fulldoi: https://doi.org/10.1142/S0218202526500508
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2502.09550
mathsc:
- 65N30
- 76D07
- 76M10
month: '08'
oa: 1
oa_version: Preprint
publication: Mathematical Models and Methods in Applied Sciences
publication_identifier:
eissn:
- 1793-6314
issn:
- 0218-2025
publication_status: epub_ahead
publisher: World Scientific Publishing
quality_controlled: '1'
scopus_import: '1'
status: public
title: A Nitsche method for incompressible fluids with general dynamic boundary conditions
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2026'
...
---
OA_place: publisher
OA_type: hybrid
_id: '19027'
abstract:
- lang: eng
text: 'Stochastic PDEs of fluctuating hydrodynamics are a powerful tool for the
description of fluctuations in many-particle systems. In this paper, we develop
and analyze a multilevel Monte Carlo (MLMC) scheme for the Dean–Kawasaki equation,
a pivotal representative of this class of SPDEs. We prove analytically and demonstrate
numerically that our MLMC scheme provides a significant reduction in computational
cost (with respect to a standard Monte Carlo method) in the simulation of the
Dean–Kawasaki equation. Specifically, we link this reduction in cost to having
a sufficiently large average particle density and show that sizeable cost reductions
can be obtained even when we have solutions with regions of low density. Numerical
simulations are provided in the two-dimensional case, confirming our theoretical
predictions. Our results are formulated entirely in terms of the law of distributions
rather than in terms of strong spatial norms: this crucially allows for MLMC speed-ups
altogether despite the Dean–Kawasaki equation being highly singular.'
acknowledgement: The work of the authors was supported by the Austrian Science Fund
(FWF) projectF65.
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Federico
full_name: Cornalba, Federico
id: 2CEB641C-A400-11E9-A717-D712E6697425
last_name: Cornalba
orcid: 0000-0002-6269-5149
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
citation:
ama: Cornalba F, Fischer JL. Multilevel Monte Carlo methods for the Dean–Kawasaki
equation from fluctuating hydrodynamics. SIAM Journal on Numerical Analysis.
2025;63(1):262-287. doi:10.1137/23M1617345
apa: Cornalba, F., & Fischer, J. L. (2025). Multilevel Monte Carlo methods for
the Dean–Kawasaki equation from fluctuating hydrodynamics. SIAM Journal on
Numerical Analysis. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/23M1617345
chicago: Cornalba, Federico, and Julian L Fischer. “Multilevel Monte Carlo Methods
for the Dean–Kawasaki Equation from Fluctuating Hydrodynamics.” SIAM Journal
on Numerical Analysis. Society for Industrial and Applied Mathematics, 2025.
https://doi.org/10.1137/23M1617345.
ieee: F. Cornalba and J. L. Fischer, “Multilevel Monte Carlo methods for the Dean–Kawasaki
equation from fluctuating hydrodynamics,” SIAM Journal on Numerical Analysis,
vol. 63, no. 1. Society for Industrial and Applied Mathematics, pp. 262–287, 2025.
ista: Cornalba F, Fischer JL. 2025. Multilevel Monte Carlo methods for the Dean–Kawasaki
equation from fluctuating hydrodynamics. SIAM Journal on Numerical Analysis. 63(1),
262–287.
mla: Cornalba, Federico, and Julian L. Fischer. “Multilevel Monte Carlo Methods
for the Dean–Kawasaki Equation from Fluctuating Hydrodynamics.” SIAM Journal
on Numerical Analysis, vol. 63, no. 1, Society for Industrial and Applied
Mathematics, 2025, pp. 262–87, doi:10.1137/23M1617345.
short: F. Cornalba, J.L. Fischer, SIAM Journal on Numerical Analysis 63 (2025) 262–287.
corr_author: '1'
date_created: 2025-02-16T23:02:34Z
date_published: 2025-02-01T00:00:00Z
date_updated: 2025-09-30T10:30:31Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1137/23M1617345
external_id:
arxiv:
- '2311.08872'
isi:
- '001447583400011'
file:
- access_level: open_access
checksum: 53505647e848ed50f7e0d00c369b14e7
content_type: application/pdf
creator: dernst
date_created: 2025-02-17T08:32:23Z
date_updated: 2025-02-17T08:32:23Z
file_id: '19029'
file_name: 2025_SIAMNumerAnaly_Cornalba.pdf
file_size: 2435019
relation: main_file
success: 1
file_date_updated: 2025-02-17T08:32:23Z
fulldoi: https://doi.org/10.1137/23M1617345
has_accepted_license: '1'
intvolume: ' 63'
isi: 1
issue: '1'
language:
- iso: eng
month: '02'
oa: 1
oa_version: Published Version
page: 262-287
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: SIAM Journal on Numerical Analysis
publication_identifier:
eissn:
- 1095-7170
issn:
- 0036-1429
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
scopus_import: '1'
status: public
title: Multilevel Monte Carlo methods for the Dean–Kawasaki equation from fluctuating
hydrodynamics
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 63
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '19505'
abstract:
- lang: eng
text: In this paper, we introduce and study the primitive equations with non-isothermal
turbulent pressure and transport noise. They are derived from the Navier–Stokes
equations by employing stochastic versions of the Boussinesq and the hydrostatic
approximations. The temperature dependence of the turbulent pressure can be seen
as a consequence of an additive noise acting on the small vertical dynamics. For
such a model we prove global well-posedness in H^1 where the noise is considered
in both the Itô and Stratonovich formulations. Compared to previous variants of
the primitive equations, the one considered here presents a more intricate coupling
between the velocity field and the temperature. The corresponding analysis is
seriously more involved than in the deterministic setting. Finally, the continuous
dependence on the initial data and the energy estimates proven here are new, even
in the case of isothermal turbulent pressure.
acknowledgement: "The first author thanks Umberto Pappalettera for helpful suggestions
on Section 2 and for bringing to his attention the reference [56]. The first author
is grateful to Marco Romito for helpful comments related to Remarks 2.1 and 2.2.
Finally, the first author thanks Caterina Balzotti for her support in creating the
picture.\r\nAntonio Agresti has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No 948819). Antonio Agresti is a member of GNAMPA (INδAM).\r\nMatthias
Hieber gratefully acknowledges the support by the Deutsche Forschungsgemeinschaft
(DFG) through the Research Unit 5528—project number 500072446.\r\nAmru Hussein has
been supported by Deutsche Forschungsgemeinschaft (DFG)—project\r\nnumber 508634462
and by MathApp—Mathematics Applied to Real-World Problems—part\r\nof the Research
Initiative of the Federal State of Rhineland-Palatinate, Germany.\r\nMartin Saal
has been supported by Deutsche Forschungsgemeinschaft (DFG)—project\r\nnumber 429483464."
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Antonio
full_name: Agresti, Antonio
id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72
last_name: Agresti
orcid: 0000-0002-9573-2962
- first_name: Matthias
full_name: Hieber, Matthias
last_name: Hieber
- first_name: Amru
full_name: Hussein, Amru
last_name: Hussein
- first_name: Martin
full_name: Saal, Martin
last_name: Saal
citation:
ama: Agresti A, Hieber M, Hussein A, Saal M. The stochastic primitive equations
with nonisothermal turbulent pressure. Annals of Applied Probability. 2025;35(1):635-700.
doi:10.1214/24-AAP2124
apa: Agresti, A., Hieber, M., Hussein, A., & Saal, M. (2025). The stochastic
primitive equations with nonisothermal turbulent pressure. Annals of Applied
Probability. Institute of Mathematical Statistics. https://doi.org/10.1214/24-AAP2124
chicago: Agresti, Antonio, Matthias Hieber, Amru Hussein, and Martin Saal. “The
Stochastic Primitive Equations with Nonisothermal Turbulent Pressure.” Annals
of Applied Probability. Institute of Mathematical Statistics, 2025. https://doi.org/10.1214/24-AAP2124.
ieee: A. Agresti, M. Hieber, A. Hussein, and M. Saal, “The stochastic primitive
equations with nonisothermal turbulent pressure,” Annals of Applied Probability,
vol. 35, no. 1. Institute of Mathematical Statistics, pp. 635–700, 2025.
ista: Agresti A, Hieber M, Hussein A, Saal M. 2025. The stochastic primitive equations
with nonisothermal turbulent pressure. Annals of Applied Probability. 35(1), 635–700.
mla: Agresti, Antonio, et al. “The Stochastic Primitive Equations with Nonisothermal
Turbulent Pressure.” Annals of Applied Probability, vol. 35, no. 1, Institute
of Mathematical Statistics, 2025, pp. 635–700, doi:10.1214/24-AAP2124.
short: A. Agresti, M. Hieber, A. Hussein, M. Saal, Annals of Applied Probability
35 (2025) 635–700.
date_created: 2025-04-06T22:01:32Z
date_published: 2025-02-01T00:00:00Z
date_updated: 2025-09-30T11:23:58Z
day: '01'
department:
- _id: JuFi
doi: 10.1214/24-AAP2124
ec_funded: 1
external_id:
arxiv:
- '2210.05973'
isi:
- '001434322900016'
fulldoi: https://doi.org/10.1214/24-AAP2124
intvolume: ' 35'
isi: 1
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2210.05973
month: '02'
oa: 1
oa_version: Preprint
page: 635-700
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Annals of Applied Probability
publication_identifier:
issn:
- 1050-5164
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
scopus_import: '1'
status: public
title: The stochastic primitive equations with nonisothermal turbulent pressure
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 35
year: '2025'
...
---
OA_place: publisher
OA_type: hybrid
_id: '19783'
abstract:
- lang: eng
text: We consider a local Cahn–Hilliard‐type model for tumor growth as well as a
nonlocal model where, compared to the local system, the Laplacian in the equation
for the chemical potential is replaced by a nonlocal operator. The latter is defined
as a convolution integral with suitable kernels parametrized by a small parameter.
For sufficiently smooth bounded domains in three dimensions, we prove convergence
of weak solutions of the nonlocal model toward strong solutions of the local model
together with convergence rates with respect to the small parameter. The proof
is done via a Gronwall‐type argument and a convergence result with rates for the
nonlocal integral operator toward the Laplacian due to Abels and Hurm.
acknowledgement: C. Hurm was partially supported by the Graduiertenkolleg 2339 IntComSin
of the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)–Project-ID
321821685. M. Moser has received funding from the European Research Council (ERC)
under the European Union's Horizon 2020 research and innovation programme (grant
agreement No 948819). The support is gratefully acknowledged. Finally, we thank
Daniel Böhme and Jonas Stange for careful proofreading. Open Access funding enabled
and organized by Projekt DEAL.
article_number: e70003
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Christoph
full_name: Hurm, Christoph
last_name: Hurm
- first_name: Maximilian
full_name: Moser, Maximilian
id: a60047a9-da77-11eb-85b4-c4dc385ebb8c
last_name: Moser
citation:
ama: Hurm C, Moser M. Nonlocal‐to‐local convergence for a Cahn–Hilliard tumor growth
model. GAMM-Mitteilungen. 2025;48(2). doi:10.1002/gamm.70003
apa: Hurm, C., & Moser, M. (2025). Nonlocal‐to‐local convergence for a Cahn–Hilliard
tumor growth model. GAMM-Mitteilungen. Wiley. https://doi.org/10.1002/gamm.70003
chicago: Hurm, Christoph, and Maximilian Moser. “Nonlocal‐to‐local Convergence for
a Cahn–Hilliard Tumor Growth Model.” GAMM-Mitteilungen. Wiley, 2025. https://doi.org/10.1002/gamm.70003.
ieee: C. Hurm and M. Moser, “Nonlocal‐to‐local convergence for a Cahn–Hilliard tumor
growth model,” GAMM-Mitteilungen, vol. 48, no. 2. Wiley, 2025.
ista: Hurm C, Moser M. 2025. Nonlocal‐to‐local convergence for a Cahn–Hilliard tumor
growth model. GAMM-Mitteilungen. 48(2), e70003.
mla: Hurm, Christoph, and Maximilian Moser. “Nonlocal‐to‐local Convergence for a
Cahn–Hilliard Tumor Growth Model.” GAMM-Mitteilungen, vol. 48, no. 2, e70003,
Wiley, 2025, doi:10.1002/gamm.70003.
short: C. Hurm, M. Moser, GAMM-Mitteilungen 48 (2025).
date_created: 2025-06-03T08:58:01Z
date_published: 2025-06-01T00:00:00Z
date_updated: 2025-06-03T09:14:17Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1002/gamm.70003
ec_funded: 1
external_id:
arxiv:
- '2402.13790'
file:
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checksum: 6bac9d3e566b68519ae80ac8b0f41f20
content_type: application/pdf
creator: dernst
date_created: 2025-06-03T09:12:22Z
date_updated: 2025-06-03T09:12:22Z
file_id: '19786'
file_name: 2025_GAMM_Hurm.pdf
file_size: 513741
relation: main_file
success: 1
file_date_updated: 2025-06-03T09:12:22Z
fulldoi: https://doi.org/10.1002/gamm.70003
has_accepted_license: '1'
intvolume: ' 48'
issue: '2'
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: GAMM-Mitteilungen
publication_identifier:
eissn:
- 1522-2608
issn:
- 0936-7195
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: Nonlocal‐to‐local convergence for a Cahn–Hilliard tumor growth model
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 48
year: '2025'
...
---
OA_place: repository
OA_type: green
_id: '10011'
abstract:
- lang: eng
text: We propose a new weak solution concept for (two-phase) mean curvature flow
which enjoys both (unconditional) existence and (weak-strong) uniqueness properties.
These solutions are evolving varifolds, just as in Brakke's formulation, but are
coupled to the phase volumes by a simple transport equation. First, we show that,
in the exact same setup as in Ilmanen's proof [J. Differential Geom. 38, 417-461,
(1993)], any limit point of solutions to the Allen-Cahn equation is a varifold
solution in our sense. Second, we prove that any calibrated flow in the sense
of Fischer et al. [arXiv:2003.05478] - and hence any classical solution to mean
curvature flow-is unique in the class of our new varifold solutions. This is in
sharp contrast to the case of Brakke flows, which a priori may disappear at any
given time and are therefore fatally non-unique. Finally, we propose an extension
of the solution concept to the multi-phase case which is at least guaranteed to
satisfy a weak-strong uniqueness principle.
acknowledgement: This project has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No 948819), and from the Deutsche Forschungsgemeinschaft (DFG,
German Research Foundation) under Germany’s Excellence Strategy – EXC-2047/1 – 390685813.
The content of this paper was developed and parts of it were written during a visit
of the first author to the Hausdorff Center of Mathematics (HCM), University of
Bonn. The hospitality and the support of HCM are gratefully acknowledged.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
- first_name: Tim
full_name: Laux, Tim
last_name: Laux
citation:
ama: 'Hensel S, Laux T. A new varifold solution concept for mean curvature flow:
Convergence of the Allen-Cahn equation and weak-strong uniqueness. Journal
of Differential Geometry. 2025;130:209-268. doi:10.4310/jdg/1747065796'
apa: 'Hensel, S., & Laux, T. (2025). A new varifold solution concept for mean
curvature flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness.
Journal of Differential Geometry. International Press of Boston. https://doi.org/10.4310/jdg/1747065796'
chicago: 'Hensel, Sebastian, and Tim Laux. “A New Varifold Solution Concept for
Mean Curvature Flow: Convergence of the Allen-Cahn Equation and Weak-Strong Uniqueness.”
Journal of Differential Geometry. International Press of Boston, 2025.
https://doi.org/10.4310/jdg/1747065796.'
ieee: 'S. Hensel and T. Laux, “A new varifold solution concept for mean curvature
flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness,” Journal
of Differential Geometry, vol. 130. International Press of Boston, pp. 209–268,
2025.'
ista: 'Hensel S, Laux T. 2025. A new varifold solution concept for mean curvature
flow: Convergence of the Allen-Cahn equation and weak-strong uniqueness. Journal
of Differential Geometry. 130, 209–268.'
mla: 'Hensel, Sebastian, and Tim Laux. “A New Varifold Solution Concept for Mean
Curvature Flow: Convergence of the Allen-Cahn Equation and Weak-Strong Uniqueness.”
Journal of Differential Geometry, vol. 130, International Press of Boston,
2025, pp. 209–68, doi:10.4310/jdg/1747065796.'
short: S. Hensel, T. Laux, Journal of Differential Geometry 130 (2025) 209–268.
corr_author: '1'
das_tickbox: '1'
date_created: 2021-09-13T12:17:10Z
date_published: 2025-05-01T00:00:00Z
date_updated: 2026-07-06T13:37:21Z
day: '01'
department:
- _id: JuFi
doi: 10.4310/jdg/1747065796
ec_funded: 1
external_id:
arxiv:
- '2109.04233'
fulldoi: https://doi.org/10.4310/jdg/1747065796
intvolume: ' 130'
keyword:
- Mean curvature flow
- gradient flows
- varifolds
- weak solutions
- weak-strong uniqueness
- calibrated geometry
- gradient-flow calibrations
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2109.04233
month: '05'
oa: 1
oa_version: Preprint
page: 209-268
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Journal of Differential Geometry
publication_identifier:
eissn:
- 1945-743X
issn:
- 0022-040X
publication_status: published
publisher: International Press of Boston
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'A new varifold solution concept for mean curvature flow: Convergence of the
Allen-Cahn equation and weak-strong uniqueness'
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 130
year: '2025'
...
---
_id: '14451'
abstract:
- lang: eng
text: 'We investigate the potential of Multi-Objective, Deep Reinforcement Learning
for stock and cryptocurrency single-asset trading: in particular, we consider
a Multi-Objective algorithm which generalizes the reward functions and discount
factor (i.e., these components are not specified a priori, but incorporated in
the learning process). Firstly, using several important assets (BTCUSD, ETHUSDT,
XRPUSDT, AAPL, SPY, NIFTY50), we verify the reward generalization property of
the proposed Multi-Objective algorithm, and provide preliminary statistical evidence
showing increased predictive stability over the corresponding Single-Objective
strategy. Secondly, we show that the Multi-Objective algorithm has a clear edge
over the corresponding Single-Objective strategy when the reward mechanism is
sparse (i.e., when non-null feedback is infrequent over time). Finally, we discuss
the generalization properties with respect to the discount factor. The entirety
of our code is provided in open-source format.'
acknowledgement: Open access funding provided by Università degli Studi di Trieste
within the CRUI-CARE Agreement. Funding was provided by Austrian Science Fund (Grant
No. F65), Horizon 2020 (Grant No. 754411) and Österreichische Forschungsförderungsgesellschaft.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Federico
full_name: Cornalba, Federico
id: 2CEB641C-A400-11E9-A717-D712E6697425
last_name: Cornalba
orcid: 0000-0002-6269-5149
- first_name: Constantin
full_name: Disselkamp, Constantin
last_name: Disselkamp
- first_name: Davide
full_name: Scassola, Davide
last_name: Scassola
- first_name: Christopher
full_name: Helf, Christopher
last_name: Helf
citation:
ama: 'Cornalba F, Disselkamp C, Scassola D, Helf C. Multi-objective reward generalization:
Improving performance of Deep Reinforcement Learning for applications in single-asset
trading. Neural Computing and Applications. 2024;36(2):617-637. doi:10.1007/s00521-023-09033-7'
apa: 'Cornalba, F., Disselkamp, C., Scassola, D., & Helf, C. (2024). Multi-objective
reward generalization: Improving performance of Deep Reinforcement Learning for
applications in single-asset trading. Neural Computing and Applications.
Springer Nature. https://doi.org/10.1007/s00521-023-09033-7'
chicago: 'Cornalba, Federico, Constantin Disselkamp, Davide Scassola, and Christopher
Helf. “Multi-Objective Reward Generalization: Improving Performance of Deep Reinforcement
Learning for Applications in Single-Asset Trading.” Neural Computing and Applications.
Springer Nature, 2024. https://doi.org/10.1007/s00521-023-09033-7.'
ieee: 'F. Cornalba, C. Disselkamp, D. Scassola, and C. Helf, “Multi-objective reward
generalization: Improving performance of Deep Reinforcement Learning for applications
in single-asset trading,” Neural Computing and Applications, vol. 36, no.
2. Springer Nature, pp. 617–637, 2024.'
ista: 'Cornalba F, Disselkamp C, Scassola D, Helf C. 2024. Multi-objective reward
generalization: Improving performance of Deep Reinforcement Learning for applications
in single-asset trading. Neural Computing and Applications. 36(2), 617–637.'
mla: 'Cornalba, Federico, et al. “Multi-Objective Reward Generalization: Improving
Performance of Deep Reinforcement Learning for Applications in Single-Asset Trading.”
Neural Computing and Applications, vol. 36, no. 2, Springer Nature, 2024,
pp. 617–37, doi:10.1007/s00521-023-09033-7.'
short: F. Cornalba, C. Disselkamp, D. Scassola, C. Helf, Neural Computing and Applications
36 (2024) 617–637.
corr_author: '1'
das_tickbox: '1'
dataavailabilitystatement: All datasets and the entire source code used in this paper
are available in open-source format at the repository https://github.com/trality/fire
. In particular, the instructions for reproducibility are contained in the README.md
file therein.
date_created: 2023-10-22T22:01:16Z
date_published: 2024-01-01T00:00:00Z
date_updated: 2026-10-15T09:42:15Z
day: '01'
ddc:
- '000'
department:
- _id: JuFi
doi: 10.1007/s00521-023-09033-7
ec_funded: 1
external_id:
arxiv:
- '2203.04579'
pmid:
- '38187995'
file:
- access_level: open_access
checksum: 04573d8e74c6119b97c2ca0a984e19a1
content_type: application/pdf
creator: dernst
date_created: 2024-07-16T08:08:54Z
date_updated: 2024-07-16T08:08:54Z
file_id: '17251'
file_name: 2024_NeuralCompApplications_Cornalba.pdf
file_size: 4412285
relation: main_file
success: 1
file_date_updated: 2024-07-16T08:08:54Z
fulldoi: https://doi.org/10.1007/s00521-023-09033-7
has_accepted_license: '1'
intvolume: ' 36'
issue: '2'
language:
- iso: eng
month: '01'
oa: 1
oa_version: Published Version
page: 617-637
pmid: 1
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
publication: Neural Computing and Applications
publication_identifier:
eissn:
- 1433-3058
issn:
- 0941-0643
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
researchdata_availability: yes
scopus_import: '1'
status: public
supplementarymaterial: no
title: 'Multi-objective reward generalization: Improving performance of Deep Reinforcement
Learning for applications in single-asset trading'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 36
year: '2024'
...
---
_id: '17887'
abstract:
- lang: eng
text: We show convergence of the Navier-Stokes/Allen-Cahn system to a classical
sharp interface model for the two-phase flow of two viscous incompressible fluids
with same viscosities in a smooth bounded domain in two and three space dimensions
as long as a smooth solution of the limit system exists. Moreover, we obtain error
estimates with the aid of a relative entropy method. Our results hold provided
that the mobility mε>0 in the Allen-Cahn equation tends to zero in a subcritical
way, i.e., mε=m0εβ for some β∈(0,2) and m0>0 . The proof proceeds by showing
via a relative entropy argument that the solution to the Navier-Stokes/Allen-Cahn
system remains close to the solution of a perturbed version of the two-phase flow
problem, augmented by an extra mean curvature flow term mεHΓt in the interface
motion. In a second step, it is easy to see that the solution to the perturbed
problem is close to the original two-phase flow.
acknowledgement: "J. Fischer and M. Moser have received funding from the European
Research Council (ERC) under the European Union’s Horizon 2020 research and innovation
programme (grant agreement No 948819).\r\nOpen Access funding enabled and organized
by Projekt DEAL."
article_number: '77'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Helmut
full_name: Abels, Helmut
last_name: Abels
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
- first_name: Maximilian
full_name: Moser, Maximilian
id: a60047a9-da77-11eb-85b4-c4dc385ebb8c
last_name: Moser
citation:
ama: Abels H, Fischer JL, Moser M. Approximation of classical two-phase flows of
viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system. Archive
for Rational Mechanics and Analysis. 2024;248(5). doi:10.1007/s00205-024-02020-9
apa: Abels, H., Fischer, J. L., & Moser, M. (2024). Approximation of classical
two-phase flows of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn
system. Archive for Rational Mechanics and Analysis. Springer Nature. https://doi.org/10.1007/s00205-024-02020-9
chicago: Abels, Helmut, Julian L Fischer, and Maximilian Moser. “Approximation of
Classical Two-Phase Flows of Viscous Incompressible Fluids by a Navier–Stokes/Allen–Cahn
System.” Archive for Rational Mechanics and Analysis. Springer Nature,
2024. https://doi.org/10.1007/s00205-024-02020-9.
ieee: H. Abels, J. L. Fischer, and M. Moser, “Approximation of classical two-phase
flows of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system,”
Archive for Rational Mechanics and Analysis, vol. 248, no. 5. Springer
Nature, 2024.
ista: Abels H, Fischer JL, Moser M. 2024. Approximation of classical two-phase flows
of viscous incompressible fluids by a Navier–Stokes/Allen–Cahn system. Archive
for Rational Mechanics and Analysis. 248(5), 77.
mla: Abels, Helmut, et al. “Approximation of Classical Two-Phase Flows of Viscous
Incompressible Fluids by a Navier–Stokes/Allen–Cahn System.” Archive for Rational
Mechanics and Analysis, vol. 248, no. 5, 77, Springer Nature, 2024, doi:10.1007/s00205-024-02020-9.
short: H. Abels, J.L. Fischer, M. Moser, Archive for Rational Mechanics and Analysis
248 (2024).
das_tickbox: '1'
dataavailabilitystatement: There is no associated data to the manuscript.
date_created: 2024-09-08T22:01:10Z
date_published: 2024-09-03T00:00:00Z
date_updated: 2026-10-15T09:44:17Z
day: '03'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00205-024-02020-9
ec_funded: 1
external_id:
arxiv:
- '2311.02997'
isi:
- '001305530600001'
pmid:
- '39239088'
file:
- access_level: open_access
checksum: 98493a05b84e4513b6394dfad4851ddf
content_type: application/pdf
creator: dernst
date_created: 2024-09-09T08:43:32Z
date_updated: 2024-09-09T08:43:32Z
file_id: '17938'
file_name: 2024_ArchiveRatAnalysis_Abels.pdf
file_size: 811131
relation: main_file
success: 1
file_date_updated: 2024-09-09T08:43:32Z
fulldoi: https://doi.org/10.1007/s00205-024-02020-9
has_accepted_license: '1'
intvolume: ' 248'
isi: 1
issue: '5'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
pmid: 1
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Archive for Rational Mechanics and Analysis
publication_identifier:
eissn:
- 1432-0673
issn:
- 0003-9527
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
researchdata_availability: not applicable
scopus_import: '1'
status: public
supplementarymaterial: no
title: Approximation of classical two-phase flows of viscous incompressible fluids
by a Navier–Stokes/Allen–Cahn system
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 248
year: '2024'
...
---
_id: '12485'
abstract:
- lang: eng
text: In this paper we introduce the critical variational setting for parabolic
stochastic evolution equations of quasi- or semi-linear type. Our results improve
many of the abstract results in the classical variational setting. In particular,
we are able to replace the usual weak or local monotonicity condition by a more
flexible local Lipschitz condition. Moreover, the usual growth conditions on the
multiplicative noise are weakened considerably. Our new setting provides general
conditions under which local and global existence and uniqueness hold. Moreover,
we prove continuous dependence on the initial data. We show that many classical
SPDEs, which could not be covered by the classical variational setting, do fit
in the critical variational setting. In particular, this is the case for the Cahn-Hilliard
equations, tamed Navier-Stokes equations, and Allen-Cahn equation.
acknowledgement: The first author has received funding from the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation programme
(grant agreement No 948819) . The second author is supported by the VICI subsidy
VI.C.212.027 of the Netherlands Organisation for Scientific Research (NWO).
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Antonio
full_name: Agresti, Antonio
id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72
last_name: Agresti
orcid: 0000-0002-9573-2962
- first_name: Mark
full_name: Veraar, Mark
last_name: Veraar
citation:
ama: Agresti A, Veraar M. The critical variational setting for stochastic evolution
equations. Probability Theory and Related Fields. 2024;188:957-1015. doi:10.1007/s00440-023-01249-x
apa: Agresti, A., & Veraar, M. (2024). The critical variational setting for
stochastic evolution equations. Probability Theory and Related Fields.
Springer Nature. https://doi.org/10.1007/s00440-023-01249-x
chicago: Agresti, Antonio, and Mark Veraar. “The Critical Variational Setting for
Stochastic Evolution Equations.” Probability Theory and Related Fields.
Springer Nature, 2024. https://doi.org/10.1007/s00440-023-01249-x.
ieee: A. Agresti and M. Veraar, “The critical variational setting for stochastic
evolution equations,” Probability Theory and Related Fields, vol. 188.
Springer Nature, pp. 957–1015, 2024.
ista: Agresti A, Veraar M. 2024. The critical variational setting for stochastic
evolution equations. Probability Theory and Related Fields. 188, 957–1015.
mla: Agresti, Antonio, and Mark Veraar. “The Critical Variational Setting for Stochastic
Evolution Equations.” Probability Theory and Related Fields, vol. 188,
Springer Nature, 2024, pp. 957–1015, doi:10.1007/s00440-023-01249-x.
short: A. Agresti, M. Veraar, Probability Theory and Related Fields 188 (2024) 957–1015.
das_tickbox: '1'
dataavailabilitystatement: Data sharing not applicable to this article as no datasets
were generated or analysed during the current study.
date_created: 2023-02-02T10:45:15Z
date_published: 2024-04-01T00:00:00Z
date_updated: 2026-10-15T09:45:31Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00440-023-01249-x
ec_funded: 1
external_id:
arxiv:
- '2206.00230'
isi:
- '001154226500001'
file:
- access_level: open_access
checksum: b8572339dbc5b8de4934dc5fd34afc7d
content_type: application/pdf
creator: dernst
date_created: 2024-07-22T09:21:09Z
date_updated: 2024-07-22T09:21:09Z
file_id: '17296'
file_name: 2024_ProbTheory_Agresti.pdf
file_size: 942801
relation: main_file
success: 1
file_date_updated: 2024-07-22T09:21:09Z
fulldoi: https://doi.org/10.1007/s00440-023-01249-x
has_accepted_license: '1'
intvolume: ' 188'
isi: 1
language:
- iso: eng
month: '04'
oa: 1
oa_version: Published Version
page: 957-1015
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- 1432-2064
issn:
- 0178-8051
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
researchdata_availability: not applicable
scopus_import: '1'
status: public
supplementarymaterial: no
title: The critical variational setting for stochastic evolution equations
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 188
year: '2024'
...
---
_id: '12178'
abstract:
- lang: eng
text: In this paper we consider the stochastic primitive equation for geophysical
flows subject to transport noise and turbulent pressure. Admitting very rough
noise terms, the global existence and uniqueness of solutions to this stochastic
partial differential equation are proven using stochastic maximal L² regularity,
the theory of critical spaces for stochastic evolution equations, and global a
priori bounds. Compared to other results in this direction, we do not need any
smallness assumption on the transport noise which acts directly on the velocity
field and we also allow rougher noise terms. The adaptation to Stratonovich type
noise and, more generally, to variable viscosity and/or conductivity are discussed
as well.
acknowledgement: The authors thank the anonymous referees for their helpful comments
and suggestions. Open Access funding enabled and organized by Projekt DEAL.
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Antonio
full_name: Agresti, Antonio
id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72
last_name: Agresti
orcid: 0000-0002-9573-2962
- first_name: Matthias
full_name: Hieber, Matthias
last_name: Hieber
- first_name: Amru
full_name: Hussein, Amru
last_name: Hussein
- first_name: Martin
full_name: Saal, Martin
last_name: Saal
citation:
ama: 'Agresti A, Hieber M, Hussein A, Saal M. The stochastic primitive equations
with transport noise and turbulent pressure. Stochastics and Partial Differential
Equations: Analysis and Computations. 2024;12:53-133. doi:10.1007/s40072-022-00277-3'
apa: 'Agresti, A., Hieber, M., Hussein, A., & Saal, M. (2024). The stochastic
primitive equations with transport noise and turbulent pressure. Stochastics
and Partial Differential Equations: Analysis and Computations. Springer Nature.
https://doi.org/10.1007/s40072-022-00277-3'
chicago: 'Agresti, Antonio, Matthias Hieber, Amru Hussein, and Martin Saal. “The
Stochastic Primitive Equations with Transport Noise and Turbulent Pressure.” Stochastics
and Partial Differential Equations: Analysis and Computations. Springer Nature,
2024. https://doi.org/10.1007/s40072-022-00277-3.'
ieee: 'A. Agresti, M. Hieber, A. Hussein, and M. Saal, “The stochastic primitive
equations with transport noise and turbulent pressure,” Stochastics and Partial
Differential Equations: Analysis and Computations, vol. 12. Springer Nature,
pp. 53–133, 2024.'
ista: 'Agresti A, Hieber M, Hussein A, Saal M. 2024. The stochastic primitive equations
with transport noise and turbulent pressure. Stochastics and Partial Differential
Equations: Analysis and Computations. 12, 53–133.'
mla: 'Agresti, Antonio, et al. “The Stochastic Primitive Equations with Transport
Noise and Turbulent Pressure.” Stochastics and Partial Differential Equations:
Analysis and Computations, vol. 12, Springer Nature, 2024, pp. 53–133, doi:10.1007/s40072-022-00277-3.'
short: 'A. Agresti, M. Hieber, A. Hussein, M. Saal, Stochastics and Partial Differential
Equations: Analysis and Computations 12 (2024) 53–133.'
das_tickbox: '1'
dataavailabilitystatement: This manuscript has no associated data.
date_created: 2023-01-12T12:12:29Z
date_published: 2024-03-01T00:00:00Z
date_updated: 2026-10-15T09:44:54Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s40072-022-00277-3
external_id:
arxiv:
- '2109.09561'
isi:
- '000874389000001'
file:
- access_level: open_access
checksum: 59c9000761134d681bdf9d482664044c
content_type: application/pdf
creator: dernst
date_created: 2024-07-22T09:29:48Z
date_updated: 2024-07-22T09:29:48Z
file_id: '17297'
file_name: 2024_StochasticsEquations_Agresti.pdf
file_size: 1206413
relation: main_file
success: 1
file_date_updated: 2024-07-22T09:29:48Z
fulldoi: https://doi.org/10.1007/s40072-022-00277-3
has_accepted_license: '1'
intvolume: ' 12'
isi: 1
keyword:
- Applied Mathematics
- Modeling and Simulation
- Statistics and Probability
language:
- iso: eng
month: '03'
oa: 1
oa_version: Published Version
page: 53-133
publication: 'Stochastics and Partial Differential Equations: Analysis and Computations'
publication_identifier:
eissn:
- 2194-041X
issn:
- 2194-0401
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
researchdata_availability: not applicable
scopus_import: '1'
status: public
supplementarymaterial: yes
title: The stochastic primitive equations with transport noise and turbulent pressure
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 12
year: '2024'
...
---
_id: '17372'
abstract:
- lang: eng
text: 'In this paper, we investigate the global well-posedness of reaction-diffusion
systems with transport noise on the d-dimensional torus. We show new global well-posedness
results for a large class of scalar equations (e.g. the Allen-Cahn equation),
and dissipative systems (e.g. equations in coagulation dynamics). Moreover, we
prove global well-posedness for two weakly dissipative systems: Lotka-Volterra
equations for d∈{1,2,3,4} and the Brusselator for d∈{1,2,3}. Many of the results
are also new without transport noise. The proofs are based on maximal regularity
techniques, positivity results, and sharp blow-up criteria developed in our recent
works, combined with energy estimates based on Itô''s formula and stochastic Gronwall
inequalities. Key novelties include the introduction of new Lζ -coercivity/dissipativity
conditions and the development of an Lp(Lq) -framework for systems of reaction-diffusion
equations, which are needed when treating dimensions d∈{2,3} in the case of
cubic or higher order nonlinearities.'
acknowledgement: The first author’s research was supported by the European Research
Council (ERC) under the European Union’s Horizon 2020 research and innovation programme
grant 948819. . The second author’s research was supported by the VICI subsidy VI.C.212.027
of the Netherlands Organisation for Scientific Research (NWO).
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Antonio
full_name: Agresti, Antonio
id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72
last_name: Agresti
orcid: 0000-0002-9573-2962
- first_name: Mark
full_name: Veraar, Mark
last_name: Veraar
citation:
ama: 'Agresti A, Veraar M. Reaction-diffusion equations with transport noise and
critical superlinear diffusion: Global well-posedness of weakly dissipative systems.
SIAM Journal on Mathematical Analysis. 2024;56(4):4870-4927. doi:10.1137/23M1562482'
apa: 'Agresti, A., & Veraar, M. (2024). Reaction-diffusion equations with transport
noise and critical superlinear diffusion: Global well-posedness of weakly dissipative
systems. SIAM Journal on Mathematical Analysis. Society for Industrial
and Applied Mathematics. https://doi.org/10.1137/23M1562482'
chicago: 'Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with
Transport Noise and Critical Superlinear Diffusion: Global Well-Posedness of Weakly
Dissipative Systems.” SIAM Journal on Mathematical Analysis. Society for
Industrial and Applied Mathematics, 2024. https://doi.org/10.1137/23M1562482.'
ieee: 'A. Agresti and M. Veraar, “Reaction-diffusion equations with transport noise
and critical superlinear diffusion: Global well-posedness of weakly dissipative
systems,” SIAM Journal on Mathematical Analysis, vol. 56, no. 4. Society
for Industrial and Applied Mathematics, pp. 4870–4927, 2024.'
ista: 'Agresti A, Veraar M. 2024. Reaction-diffusion equations with transport noise
and critical superlinear diffusion: Global well-posedness of weakly dissipative
systems. SIAM Journal on Mathematical Analysis. 56(4), 4870–4927.'
mla: 'Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with Transport
Noise and Critical Superlinear Diffusion: Global Well-Posedness of Weakly Dissipative
Systems.” SIAM Journal on Mathematical Analysis, vol. 56, no. 4, Society
for Industrial and Applied Mathematics, 2024, pp. 4870–927, doi:10.1137/23M1562482.'
short: A. Agresti, M. Veraar, SIAM Journal on Mathematical Analysis 56 (2024) 4870–4927.
corr_author: '1'
das_tickbox: '0'
date_created: 2024-08-04T22:01:21Z
date_published: 2024-08-01T00:00:00Z
date_updated: 2026-10-15T09:43:41Z
day: '01'
department:
- _id: JuFi
doi: 10.1137/23M1562482
ec_funded: 1
external_id:
arxiv:
- '2301.06897'
isi:
- '001315424500021'
fulldoi: https://doi.org/10.1137/23M1562482
intvolume: ' 56'
isi: 1
issue: '4'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2301.06897
month: '08'
oa: 1
oa_version: Preprint
page: 4870-4927
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: SIAM Journal on Mathematical Analysis
publication_identifier:
eissn:
- 1095-7154
issn:
- 0036-1410
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: yes
title: 'Reaction-diffusion equations with transport noise and critical superlinear
diffusion: Global well-posedness of weakly dissipative systems'
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 56
year: '2024'
...
---
_id: '14884'
abstract:
- lang: eng
text: We perform a stochastic homogenization analysis for composite materials exhibiting
a random microstructure. Under the assumptions of stationarity and ergodicity,
we characterize the Gamma-limit of a micromagnetic energy functional defined on
magnetizations taking value in the unit sphere and including both symmetric and
antisymmetric exchange contributions. This Gamma-limit corresponds to a micromagnetic
energy functional with homogeneous coefficients. We provide explicit formulas
for the effective magnetic properties of the composite material in terms of homogenization
correctors. Additionally, the variational analysis of the two exchange energy
terms is performed in the more general setting of functionals defined on manifold-valued
maps with Sobolev regularity, in the case in which the target manifold is a bounded,
orientable smooth surface with tubular neighborhood of uniform thickness. Eventually,
we present an explicit characterization of minimizers of the effective exchange
in the case of magnetic multilayers, providing quantitative evidence of Dzyaloshinskii’s
predictions on the emergence of helical structures in composite ferromagnetic
materials with stochastic microstructure.
acknowledgement: All authors acknowledge support of the Austrian Science Fund (FWF)
through the SFB project F65. The research of E. Davoli and L. D’Elia has additionally
been supported by the FWF through grants V662, Y1292, and P35359, as well as from
OeAD through the WTZ grant CZ09/2023.
article_number: '30'
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Elisa
full_name: Davoli, Elisa
last_name: Davoli
- first_name: Lorenza
full_name: D’Elia, Lorenza
last_name: D’Elia
- first_name: Jonas
full_name: Ingmanns, Jonas
id: 71523d30-15b2-11ec-abd3-f80aa909d6b0
last_name: Ingmanns
orcid: 0009-0008-1310-7946
citation:
ama: Davoli E, D’Elia L, Ingmanns J. Stochastic homogenization of micromagnetic
energies and emergence of magnetic skyrmions. Journal of Nonlinear Science.
2024;34(2). doi:10.1007/s00332-023-10005-3
apa: Davoli, E., D’Elia, L., & Ingmanns, J. (2024). Stochastic homogenization
of micromagnetic energies and emergence of magnetic skyrmions. Journal of Nonlinear
Science. Springer Nature. https://doi.org/10.1007/s00332-023-10005-3
chicago: Davoli, Elisa, Lorenza D’Elia, and Jonas Ingmanns. “Stochastic Homogenization
of Micromagnetic Energies and Emergence of Magnetic Skyrmions.” Journal of
Nonlinear Science. Springer Nature, 2024. https://doi.org/10.1007/s00332-023-10005-3.
ieee: E. Davoli, L. D’Elia, and J. Ingmanns, “Stochastic homogenization of micromagnetic
energies and emergence of magnetic skyrmions,” Journal of Nonlinear Science,
vol. 34, no. 2. Springer Nature, 2024.
ista: Davoli E, D’Elia L, Ingmanns J. 2024. Stochastic homogenization of micromagnetic
energies and emergence of magnetic skyrmions. Journal of Nonlinear Science. 34(2),
30.
mla: Davoli, Elisa, et al. “Stochastic Homogenization of Micromagnetic Energies
and Emergence of Magnetic Skyrmions.” Journal of Nonlinear Science, vol.
34, no. 2, 30, Springer Nature, 2024, doi:10.1007/s00332-023-10005-3.
short: E. Davoli, L. D’Elia, J. Ingmanns, Journal of Nonlinear Science 34 (2024).
das_tickbox: '1'
dataavailabilitystatement: Data sharing is not applicable to this article as no datasets
were generated or analyzed during the current study.
date_created: 2024-01-28T23:01:42Z
date_published: 2024-01-23T00:00:00Z
date_updated: 2026-10-15T09:46:00Z
day: '23'
department:
- _id: JuFi
doi: 10.1007/s00332-023-10005-3
external_id:
arxiv:
- '2306.05151'
isi:
- '001147480200001'
fulldoi: https://doi.org/10.1007/s00332-023-10005-3
intvolume: ' 34'
isi: 1
issue: '2'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2306.05151
month: '01'
oa: 1
oa_version: Preprint
project:
- _id: fc31cba2-9c52-11eb-aca3-ff467d239cd2
grant_number: F6504
name: Taming Complexity in Partial Differential Systems
publication: Journal of Nonlinear Science
publication_identifier:
eissn:
- 1432-1467
issn:
- 0938-8974
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
researchdata_availability: not applicable
scopus_import: '1'
status: public
supplementarymaterial: no
title: Stochastic homogenization of micromagnetic energies and emergence of magnetic
skyrmions
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 34
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '13129'
abstract:
- lang: eng
text: "We study the representative volume element (RVE) method, which is a method
to approximately infer the effective behavior ahom of a stationary random medium.
The latter is described by a coefficient field a(x) generated from a given ensemble
⟨⋅⟩ and the corresponding linear elliptic operator −∇⋅a∇. In line with the theory
of homogenization, the method proceeds by computing d=3 correctors (d denoting
the space dimension). To be numerically tractable, this computation has to be
done on a finite domain: the so-called representative volume element, i.e., a
large box with, say, periodic boundary conditions. The main message of this article
is: Periodize the ensemble instead of its realizations. By this, we mean that
it is better to sample from a suitably periodized ensemble than to periodically
extend the restriction of a realization a(x) from the whole-space ensemble ⟨⋅⟩.
We make this point by investigating the bias (or systematic error), i.e., the
difference between ahom and the expected value of the RVE method, in terms of
its scaling w.r.t. the lateral size L of the box. In case of periodizing a(x),
we heuristically argue that this error is generically O(L−1). In case of a suitable
periodization of ⟨⋅⟩\r\n, we rigorously show that it is O(L−d). In fact, we give
a characterization of the leading-order error term for both strategies and argue
that even in the isotropic case it is generically non-degenerate. We carry out
the rigorous analysis in the convenient setting of ensembles ⟨⋅⟩\r\n of Gaussian
type, which allow for a straightforward periodization, passing via the (integrable)
covariance function. This setting has also the advantage of making the Price theorem
and the Malliavin calculus available for optimal stochastic estimates of correctors.
We actually need control of second-order correctors to capture the leading-order
error term. This is due to inversion symmetry when applying the two-scale expansion
to the Green function. As a bonus, we present a stream-lined strategy to estimate
the error in a higher-order two-scale expansion of the Green function."
acknowledgement: Open access funding provided by Institute of Science and Technology
(IST Austria).
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Nicolas
full_name: Clozeau, Nicolas
id: fea1b376-906f-11eb-847d-b2c0cf46455b
last_name: Clozeau
- first_name: Marc
full_name: Josien, Marc
last_name: Josien
- first_name: Felix
full_name: Otto, Felix
last_name: Otto
- first_name: Qiang
full_name: Xu, Qiang
last_name: Xu
citation:
ama: 'Clozeau N, Josien M, Otto F, Xu Q. Bias in the representative volume element
method: Periodize the ensemble instead of its realizations. Foundations of
Computational Mathematics. 2024;24:1305-1387. doi:10.1007/s10208-023-09613-y'
apa: 'Clozeau, N., Josien, M., Otto, F., & Xu, Q. (2024). Bias in the representative
volume element method: Periodize the ensemble instead of its realizations. Foundations
of Computational Mathematics. Springer Nature. https://doi.org/10.1007/s10208-023-09613-y'
chicago: 'Clozeau, Nicolas, Marc Josien, Felix Otto, and Qiang Xu. “Bias in the
Representative Volume Element Method: Periodize the Ensemble Instead of Its Realizations.”
Foundations of Computational Mathematics. Springer Nature, 2024. https://doi.org/10.1007/s10208-023-09613-y.'
ieee: 'N. Clozeau, M. Josien, F. Otto, and Q. Xu, “Bias in the representative volume
element method: Periodize the ensemble instead of its realizations,” Foundations
of Computational Mathematics, vol. 24. Springer Nature, pp. 1305–1387, 2024.'
ista: 'Clozeau N, Josien M, Otto F, Xu Q. 2024. Bias in the representative volume
element method: Periodize the ensemble instead of its realizations. Foundations
of Computational Mathematics. 24, 1305–1387.'
mla: 'Clozeau, Nicolas, et al. “Bias in the Representative Volume Element Method:
Periodize the Ensemble Instead of Its Realizations.” Foundations of Computational
Mathematics, vol. 24, Springer Nature, 2024, pp. 1305–87, doi:10.1007/s10208-023-09613-y.'
short: N. Clozeau, M. Josien, F. Otto, Q. Xu, Foundations of Computational Mathematics
24 (2024) 1305–1387.
corr_author: '1'
das_tickbox: '0'
date_created: 2023-06-11T22:00:40Z
date_published: 2024-08-01T00:00:00Z
date_updated: 2026-10-15T09:47:37Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s10208-023-09613-y
external_id:
isi:
- '000999623100001'
file:
- access_level: open_access
checksum: ec0582e2b55e2703a7da2686ae0d682e
content_type: application/pdf
creator: dernst
date_created: 2025-01-09T07:36:57Z
date_updated: 2025-01-09T07:36:57Z
file_id: '18782'
file_name: 2024_FoundCompMath_Clozeau.pdf
file_size: 1454406
relation: main_file
success: 1
file_date_updated: 2025-01-09T07:36:57Z
fulldoi: https://doi.org/10.1007/s10208-023-09613-y
has_accepted_license: '1'
intvolume: ' 24'
isi: 1
language:
- iso: eng
month: '08'
oa: 1
oa_version: Published Version
page: 1305-1387
publication: Foundations of Computational Mathematics
publication_identifier:
eissn:
- 1615-3383
issn:
- 1615-3375
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: yes
title: 'Bias in the representative volume element method: Periodize the ensemble instead
of its realizations'
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 24
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '12486'
abstract:
- lang: eng
text: This paper is concerned with the problem of regularization by noise of systems
of reaction–diffusion equations with mass control. It is known that strong solutions
to such systems of PDEs may blow-up in finite time. Moreover, for many systems
of practical interest, establishing whether the blow-up occurs or not is an open
question. Here we prove that a suitable multiplicative noise of transport type
has a regularizing effect. More precisely, for both a sufficiently noise intensity
and a high spectrum, the blow-up of strong solutions is delayed up to an arbitrary
large time. Global existence is shown for the case of exponentially decreasing
mass. The proofs combine and extend recent developments in regularization by noise
and in the Lp(Lq)-approach to stochastic PDEs, highlighting new connections between
the two areas.
acknowledgement: "The author has received funding from the European Research Council
(ERC) under the European Union’s Horizon 2020 research and innovation programme
(Grant Agreement No. 948819).\r\nThe author thanks Lorenzo Dello Schiavo, Lucio
Galeati and Mark Veraar for helpful comments. The author acknowledges Caterina Balzotti
for her support in creating the picture. The author\r\nthanks the anonymous referee
for helpful comments. "
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Antonio
full_name: Agresti, Antonio
id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72
last_name: Agresti
orcid: 0000-0002-9573-2962
citation:
ama: 'Agresti A. Delayed blow-up and enhanced diffusion by transport noise for systems
of reaction-diffusion equations. Stochastics and Partial Differential Equations:
Analysis and Computations. 2024;12:1907-1981. doi:10.1007/s40072-023-00319-4'
apa: 'Agresti, A. (2024). Delayed blow-up and enhanced diffusion by transport noise
for systems of reaction-diffusion equations. Stochastics and Partial Differential
Equations: Analysis and Computations. Springer Nature. https://doi.org/10.1007/s40072-023-00319-4'
chicago: 'Agresti, Antonio. “Delayed Blow-up and Enhanced Diffusion by Transport
Noise for Systems of Reaction-Diffusion Equations.” Stochastics and Partial
Differential Equations: Analysis and Computations. Springer Nature, 2024.
https://doi.org/10.1007/s40072-023-00319-4.'
ieee: 'A. Agresti, “Delayed blow-up and enhanced diffusion by transport noise for
systems of reaction-diffusion equations,” Stochastics and Partial Differential
Equations: Analysis and Computations, vol. 12. Springer Nature, pp. 1907–1981,
2024.'
ista: 'Agresti A. 2024. Delayed blow-up and enhanced diffusion by transport noise
for systems of reaction-diffusion equations. Stochastics and Partial Differential
Equations: Analysis and Computations. 12, 1907–1981.'
mla: 'Agresti, Antonio. “Delayed Blow-up and Enhanced Diffusion by Transport Noise
for Systems of Reaction-Diffusion Equations.” Stochastics and Partial Differential
Equations: Analysis and Computations, vol. 12, Springer Nature, 2024, pp.
1907–81, doi:10.1007/s40072-023-00319-4.'
short: 'A. Agresti, Stochastics and Partial Differential Equations: Analysis and
Computations 12 (2024) 1907–1981.'
corr_author: '1'
das_tickbox: '1'
dataavailabilitystatement: This manuscript has no associated data.
date_created: 2023-02-02T10:45:47Z
date_published: 2024-09-01T00:00:00Z
date_updated: 2026-10-15T09:48:09Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s40072-023-00319-4
ec_funded: 1
external_id:
arxiv:
- '2207.08293'
isi:
- '001108594600001'
pmid:
- '39104877'
file:
- access_level: open_access
checksum: 3c93d07a5f7e0b0caa8062eadcfa69c2
content_type: application/pdf
creator: dernst
date_created: 2025-01-09T08:01:02Z
date_updated: 2025-01-09T08:01:02Z
file_id: '18787'
file_name: 2024_StochPartDiffEquations_Agresti.pdf
file_size: 1320682
relation: main_file
success: 1
file_date_updated: 2025-01-09T08:01:02Z
fulldoi: https://doi.org/10.1007/s40072-023-00319-4
has_accepted_license: '1'
intvolume: ' 12'
isi: 1
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 1907-1981
pmid: 1
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: 'Stochastics and Partial Differential Equations: Analysis and Computations'
publication_identifier:
eissn:
- 2194-041X
issn:
- 2194-0401
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
researchdata_availability: not applicable
scopus_import: '1'
status: public
supplementarymaterial: no
title: Delayed blow-up and enhanced diffusion by transport noise for systems of reaction-diffusion
equations
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 12
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '14797'
abstract:
- lang: eng
text: We study a random matching problem on closed compact 2 -dimensional Riemannian
manifolds (with respect to the squared Riemannian distance), with samples of random
points whose common law is absolutely continuous with respect to the volume measure
with strictly positive and bounded density. We show that given two sequences of
numbers n and m=m(n) of points, asymptotically equivalent as n goes to infinity,
the optimal transport plan between the two empirical measures μn and νm is
quantitatively well-approximated by (Id,exp(∇hn))#μn where hn solves a linear
elliptic PDE obtained by a regularized first-order linearization of the Monge-Ampère
equation. This is obtained in the case of samples of correlated random points
for which a stretched exponential decay of the α -mixing coefficient holds and
for a class of discrete-time Markov chains having a unique absolutely continuous
invariant measure with respect to the volume measure.
acknowledgement: "NC has received funding from the European Research Council (ERC)
under the European Union’s Horizon 2020 research and innovation programme (Grant
agreement No 948819).\r\nFM is supported by the Deutsche Forschungsgemeinschaft
(DFG, German Research Foundation) through the SPP 2265 Random Geometric Systems.
FM has been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research
Foundation) under Germany’s Excellence Strategy EXC 2044 -390685587, Mathematics
Münster: Dynamics–Geometry–Structure. FM has been funded by the Max Planck Institute
for Mathematics in the Sciences."
article_processing_charge: Yes (in subscription journal)
article_type: original
arxiv: 1
author:
- first_name: Nicolas
full_name: Clozeau, Nicolas
id: fea1b376-906f-11eb-847d-b2c0cf46455b
last_name: Clozeau
- first_name: Francesco
full_name: Mattesini, Francesco
last_name: Mattesini
citation:
ama: Clozeau N, Mattesini F. Annealed quantitative estimates for the quadratic 2D-discrete
random matching problem. Probability Theory and Related Fields. 2024;190:485-541.
doi:10.1007/s00440-023-01254-0
apa: Clozeau, N., & Mattesini, F. (2024). Annealed quantitative estimates for
the quadratic 2D-discrete random matching problem. Probability Theory and Related
Fields. Springer Nature. https://doi.org/10.1007/s00440-023-01254-0
chicago: Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates
for the Quadratic 2D-Discrete Random Matching Problem.” Probability Theory
and Related Fields. Springer Nature, 2024. https://doi.org/10.1007/s00440-023-01254-0.
ieee: N. Clozeau and F. Mattesini, “Annealed quantitative estimates for the quadratic
2D-discrete random matching problem,” Probability Theory and Related Fields,
vol. 190. Springer Nature, pp. 485–541, 2024.
ista: Clozeau N, Mattesini F. 2024. Annealed quantitative estimates for the quadratic
2D-discrete random matching problem. Probability Theory and Related Fields. 190,
485–541.
mla: Clozeau, Nicolas, and Francesco Mattesini. “Annealed Quantitative Estimates
for the Quadratic 2D-Discrete Random Matching Problem.” Probability Theory
and Related Fields, vol. 190, Springer Nature, 2024, pp. 485–541, doi:10.1007/s00440-023-01254-0.
short: N. Clozeau, F. Mattesini, Probability Theory and Related Fields 190 (2024)
485–541.
corr_author: '1'
das_tickbox: '0'
date_created: 2024-01-14T23:00:57Z
date_published: 2024-10-01T00:00:00Z
date_updated: 2026-10-15T09:48:31Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00440-023-01254-0
ec_funded: 1
external_id:
arxiv:
- '2303.00353'
isi:
- '001136206200002'
file:
- access_level: open_access
checksum: 34f44cad6a210ff66791ee37e590af2c
content_type: application/pdf
creator: dernst
date_created: 2025-01-09T08:10:54Z
date_updated: 2025-01-09T08:10:54Z
file_id: '18788'
file_name: 2024_ProbTheoryRelatFields_Clozeau.pdf
file_size: 880117
relation: main_file
success: 1
file_date_updated: 2025-01-09T08:10:54Z
fulldoi: https://doi.org/10.1007/s00440-023-01254-0
has_accepted_license: '1'
intvolume: ' 190'
isi: 1
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 485-541
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Probability Theory and Related Fields
publication_identifier:
eissn:
- 1432-2064
issn:
- 0178-8051
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Annealed quantitative estimates for the quadratic 2D-discrete random matching
problem
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 190
year: '2024'
...
---
_id: '15334'
abstract:
- lang: eng
text: We consider the sharp interface limit of a Navier-Stokes/Allen Cahn equation
in a bounded smooth domain in two space dimensions, in the case of vanishing mobility
mε=ε√, where the small parameter ε>0 related to the thickness of the diffuse interface
is sent to zero. For well-prepared initial data and sufficiently small times,
we rigorously prove convergence to the classical two-phase Navier-Stokes system
with surface tension. The idea of the proof is to use asymptotic expansions to
construct an approximate solution and to estimate the difference of the exact
and approximate solutions with a spectral estimate for the (at the approximate
solution) linearized Allen-Cahn operator. In the calculations we use a fractional
order ansatz and new ansatz terms in higher orders leading to a suitable ε-scaled
and coupled model problem. Moreover, we apply the novel idea of introducing ε-dependent
coordinates.
acknowledgement: "Open Access funding enabled and organized by Projekt DEAL.\r\nM.
Fei was partially supported by NSF of China under Grant No. 12271004 and Anhui Provincial
Funding Project under Grant Nos. gxbjZD2022009 and 2308085J10. Moreover, M. Moser
has received funding from the European Research Council (ERC) under the European
Union’s Horizon 2020 research and innovation programme (Grant Agreement No 948819)."
article_number: '94'
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Helmut
full_name: Abels, Helmut
last_name: Abels
- first_name: Mingwen
full_name: Fei, Mingwen
last_name: Fei
- first_name: Maximilian
full_name: Moser, Maximilian
id: a60047a9-da77-11eb-85b4-c4dc385ebb8c
last_name: Moser
citation:
ama: Abels H, Fei M, Moser M. Sharp interface limit for a Navier–Stokes/Allen–Cahn
system in the case of a vanishing mobility. Calculus of Variations and Partial
Differential Equations. 2024;63(4). doi:10.1007/s00526-024-02715-7
apa: Abels, H., Fei, M., & Moser, M. (2024). Sharp interface limit for a Navier–Stokes/Allen–Cahn
system in the case of a vanishing mobility. Calculus of Variations and Partial
Differential Equations. Springer Nature. https://doi.org/10.1007/s00526-024-02715-7
chicago: Abels, Helmut, Mingwen Fei, and Maximilian Moser. “Sharp Interface Limit
for a Navier–Stokes/Allen–Cahn System in the Case of a Vanishing Mobility.” Calculus
of Variations and Partial Differential Equations. Springer Nature, 2024. https://doi.org/10.1007/s00526-024-02715-7.
ieee: H. Abels, M. Fei, and M. Moser, “Sharp interface limit for a Navier–Stokes/Allen–Cahn
system in the case of a vanishing mobility,” Calculus of Variations and Partial
Differential Equations, vol. 63, no. 4. Springer Nature, 2024.
ista: Abels H, Fei M, Moser M. 2024. Sharp interface limit for a Navier–Stokes/Allen–Cahn
system in the case of a vanishing mobility. Calculus of Variations and Partial
Differential Equations. 63(4), 94.
mla: Abels, Helmut, et al. “Sharp Interface Limit for a Navier–Stokes/Allen–Cahn
System in the Case of a Vanishing Mobility.” Calculus of Variations and Partial
Differential Equations, vol. 63, no. 4, 94, Springer Nature, 2024, doi:10.1007/s00526-024-02715-7.
short: H. Abels, M. Fei, M. Moser, Calculus of Variations and Partial Differential
Equations 63 (2024).
das_tickbox: '0'
date_created: 2024-04-21T22:00:52Z
date_published: 2024-05-01T00:00:00Z
date_updated: 2026-10-15T09:47:15Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00526-024-02715-7
ec_funded: 1
external_id:
arxiv:
- '2304.12096'
isi:
- '001199418100002'
file:
- access_level: open_access
checksum: b1095fad4cae596f52cc616a973bdde2
content_type: application/pdf
creator: dernst
date_created: 2024-04-23T07:30:48Z
date_updated: 2024-04-23T07:30:48Z
file_id: '15343'
file_name: 2024_CalculusEquations_Abels.pdf
file_size: 975186
relation: main_file
success: 1
file_date_updated: 2024-04-23T07:30:48Z
fulldoi: https://doi.org/10.1007/s00526-024-02715-7
has_accepted_license: '1'
intvolume: ' 63'
isi: 1
issue: '4'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Calculus of Variations and Partial Differential Equations
publication_identifier:
eissn:
- 1432-0835
issn:
- 0944-2669
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Sharp interface limit for a Navier–Stokes/Allen–Cahn system in the case of
a vanishing mobility
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 63
year: '2024'
...
---
OA_place: publisher
OA_type: hybrid
_id: '15098'
abstract:
- lang: eng
text: The paper is devoted to the analysis of the global well-posedness and the
interior regularity of the 2D Navier–Stokes equations with inhomogeneous stochastic
boundary conditions. The noise, white in time and coloured in space, can be interpreted
as the physical law describing the driving mechanism on the atmosphere–ocean interface,
i.e. as a balance of the shear stress of the ocean and the horizontal wind force.
acknowledgement: The authors thank Professor Franco Flandoli for useful discussions
and valuable insight into the subject. In particular, A.A. would like to thank professor
Franco Flandoli for hosting and financially contributing to his research visit at
Scuola Normale di Pisa in January 2023, where this work started. E.L. would like
to express sincere gratitude to Professor Marco Fuhrman for igniting his interest
in this particular field of research. E.L. want to thank Professor Matthias Hieber
and Dr. Martin Saal for useful discussions. Finally, the authors thank the anonymous
referee for helpful comments which improved the paper from its initial version.Open
access funding provided by Scuola Normale Superiore within the CRUI-CARE Agreement.
A. Agresti has received funding from the European Research Council (ERC) under the
European Union’s Horizon 2020 research and innovation programme (Grant Agreement
No. 948819).
article_processing_charge: Yes (via OA deal)
article_type: original
arxiv: 1
author:
- first_name: Antonio
full_name: Agresti, Antonio
id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72
last_name: Agresti
orcid: 0000-0002-9573-2962
- first_name: Eliseo
full_name: Luongo, Eliseo
last_name: Luongo
citation:
ama: Agresti A, Luongo E. Global well-posedness and interior regularity of 2D Navier-Stokes
equations with stochastic boundary conditions. Mathematische Annalen. 2024;390:2727-2766.
doi:10.1007/s00208-024-02812-0
apa: Agresti, A., & Luongo, E. (2024). Global well-posedness and interior regularity
of 2D Navier-Stokes equations with stochastic boundary conditions. Mathematische
Annalen. Springer Nature. https://doi.org/10.1007/s00208-024-02812-0
chicago: Agresti, Antonio, and Eliseo Luongo. “Global Well-Posedness and Interior
Regularity of 2D Navier-Stokes Equations with Stochastic Boundary Conditions.”
Mathematische Annalen. Springer Nature, 2024. https://doi.org/10.1007/s00208-024-02812-0.
ieee: A. Agresti and E. Luongo, “Global well-posedness and interior regularity of
2D Navier-Stokes equations with stochastic boundary conditions,” Mathematische
Annalen, vol. 390. Springer Nature, pp. 2727–2766, 2024.
ista: Agresti A, Luongo E. 2024. Global well-posedness and interior regularity of
2D Navier-Stokes equations with stochastic boundary conditions. Mathematische
Annalen. 390, 2727–2766.
mla: Agresti, Antonio, and Eliseo Luongo. “Global Well-Posedness and Interior Regularity
of 2D Navier-Stokes Equations with Stochastic Boundary Conditions.” Mathematische
Annalen, vol. 390, Springer Nature, 2024, pp. 2727–66, doi:10.1007/s00208-024-02812-0.
short: A. Agresti, E. Luongo, Mathematische Annalen 390 (2024) 2727–2766.
das_tickbox: '1'
dataavailabilitystatement: Data sharing not applicable to this article as no data
sets were generated or analyzed during the current study.
date_created: 2024-03-10T23:00:54Z
date_published: 2024-10-01T00:00:00Z
date_updated: 2026-10-15T09:48:57Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00208-024-02812-0
ec_funded: 1
external_id:
arxiv:
- '2306.11081'
isi:
- '001172711400002'
pmid:
- '39351582'
file:
- access_level: open_access
checksum: d55cac8bddea09a97f06612825c4f229
content_type: application/pdf
creator: dernst
date_created: 2025-01-09T08:23:36Z
date_updated: 2025-01-09T08:23:36Z
file_id: '18790'
file_name: 2024_MathAnnalen_Agresti.pdf
file_size: 661557
relation: main_file
success: 1
file_date_updated: 2025-01-09T08:23:36Z
fulldoi: https://doi.org/10.1007/s00208-024-02812-0
has_accepted_license: '1'
intvolume: ' 390'
isi: 1
language:
- iso: eng
month: '10'
oa: 1
oa_version: Published Version
page: 2727-2766
pmid: 1
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Mathematische Annalen
publication_identifier:
eissn:
- 1432-1807
issn:
- 0025-5831
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
researchdata_availability: not applicable
scopus_import: '1'
status: public
supplementarymaterial: no
title: Global well-posedness and interior regularity of 2D Navier-Stokes equations
with stochastic boundary conditions
tmp:
image: /images/cc_by.png
legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 390
year: '2024'
...
---
OA_place: repository
OA_type: green
_id: '17462'
abstract:
- lang: eng
text: We are interested in numerical algorithms for computing the electrical field
generated by a charge distribution localized on scale l in an infinite heterogeneous
correlated random medium, in a situation where the medium is only known in a box
of diameter L >>l around the support of the charge. We show that the algorithm
in [J. Lu, F. Otto, and L. Wang, Optimal Artificial Boundary Conditions Based
on Second-Order Correctors for Three Dimensional Random Ellilptic Media, preprint,
arXiv:2109.01616, 2021], suggesting optimal Dirichlet boundary conditions motivated
by the multipole expansion [P. Bella, A. Giunti, and F. Otto, Comm. Partial Differential
Equations, 45 (2020), pp. 561–640], still performs well in correlated media. With
overwhelming probability, we obtain a convergence rate in terms of l, L, and the
size of the correlations for which optimality is supported with numerical simulations.
These estimates are provided for ensembles which satisfy a multiscale logarithmic
Sobolev inequality, where our main tool is an extension of the semigroup estimates
in [N. Clozeau, Stoch. Partial Differ. Equ. Anal. Comput., 11 (2023), pp. 1254–1378].
As part of our strategy, we construct sublinear second-order correctors in this
correlated setting, which is of independent interest.
acknowledgement: We would like to thank our affiliations, Institute of Science and
Technology Austria and Max Planck Institute for Mathematics in the Sciences, for
supporting the authors’ visits to each other, which greatly facilitated this work.
We would like to thank Marc Josien and Quinn Winters for assistance in numerical
implementation.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Nicolas
full_name: Clozeau, Nicolas
id: fea1b376-906f-11eb-847d-b2c0cf46455b
last_name: Clozeau
- first_name: Lihan
full_name: Wang, Lihan
last_name: Wang
citation:
ama: Clozeau N, Wang L. Artificial boundary conditions for random elliptic systems
with correlated coefficient field. Multiscale Modeling and Simulation.
2024;22(3):973-1029. doi:10.1137/23M1603819
apa: Clozeau, N., & Wang, L. (2024). Artificial boundary conditions for random
elliptic systems with correlated coefficient field. Multiscale Modeling and
Simulation. Society for Industrial and Applied Mathematics. https://doi.org/10.1137/23M1603819
chicago: Clozeau, Nicolas, and Lihan Wang. “Artificial Boundary Conditions for Random
Elliptic Systems with Correlated Coefficient Field.” Multiscale Modeling and
Simulation. Society for Industrial and Applied Mathematics, 2024. https://doi.org/10.1137/23M1603819.
ieee: N. Clozeau and L. Wang, “Artificial boundary conditions for random elliptic
systems with correlated coefficient field,” Multiscale Modeling and Simulation,
vol. 22, no. 3. Society for Industrial and Applied Mathematics, pp. 973–1029,
2024.
ista: Clozeau N, Wang L. 2024. Artificial boundary conditions for random elliptic
systems with correlated coefficient field. Multiscale Modeling and Simulation.
22(3), 973–1029.
mla: Clozeau, Nicolas, and Lihan Wang. “Artificial Boundary Conditions for Random
Elliptic Systems with Correlated Coefficient Field.” Multiscale Modeling and
Simulation, vol. 22, no. 3, Society for Industrial and Applied Mathematics,
2024, pp. 973–1029, doi:10.1137/23M1603819.
short: N. Clozeau, L. Wang, Multiscale Modeling and Simulation 22 (2024) 973–1029.
corr_author: '1'
das_tickbox: '0'
date_created: 2024-08-25T22:01:08Z
date_published: 2024-09-01T00:00:00Z
date_updated: 2026-10-15T09:49:19Z
day: '01'
department:
- _id: JuFi
doi: 10.1137/23M1603819
ec_funded: 1
external_id:
arxiv:
- '2309.06798'
isi:
- '001285416500001'
fulldoi: https://doi.org/10.1137/23M1603819
intvolume: ' 22'
isi: 1
issue: '3'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2309.06798
month: '09'
oa: 1
oa_version: Preprint
page: 973-1029
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Multiscale Modeling and Simulation
publication_identifier:
eissn:
- 1540-3467
issn:
- 1540-3459
publication_status: published
publisher: Society for Industrial and Applied Mathematics
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Artificial boundary conditions for random elliptic systems with correlated
coefficient field
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 22
year: '2024'
...
---
_id: '15119'
abstract:
- lang: eng
text: In this paper we consider an SPDE where the leading term is a second order
operator with periodic boundary conditions, coefficients which are measurable
in (t,ω) , and Hölder continuous in space. Assuming stochastic parabolicity conditions,
we prove Lp((0,T)×Ω,tκdt;Hσ,q(Td)) -estimates. The main novelty is that we do
not require p=q . Moreover, we allow arbitrary σ∈R and weights in time. Such
mixed regularity estimates play a crucial role in applications to nonlinear SPDEs
which is clear from our previous work. To prove our main results we develop a
general perturbation theory for SPDEs. Moreover, we prove a new result on pointwise
multiplication in spaces with fractional smoothness.
acknowledgement: The first author has been partially supported by the Nachwuchsring
– Network for the promotion of young scientists – at TU Kaiserslautern. The second
author is supported by the VIDI subsidy 639.032.427 of the Netherlands Organisation
for Scientific Research (NWO). The authors thank the anonymous referees and Max
Sauerbrey for careful reading and helpful suggestions.
article_processing_charge: No
article_type: original
arxiv: 1
author:
- first_name: Antonio
full_name: Agresti, Antonio
id: 673cd0cc-9b9a-11eb-b144-88f30e1fbb72
last_name: Agresti
orcid: 0000-0002-9573-2962
- first_name: Mark
full_name: Veraar, Mark
last_name: Veraar
citation:
ama: Agresti A, Veraar M. Stochastic maximal Lp(Lq)-regularity for second order
systems with periodic boundary conditions. Annales de l’Institut Henri Poincaré,
Probabilités et Statistiques. 2024;60(1):413-430. doi:10.1214/22-AIHP1333
apa: Agresti, A., & Veraar, M. (2024). Stochastic maximal Lp(Lq)-regularity
for second order systems with periodic boundary conditions. Annales de l’Institut
Henri Poincaré, Probabilités et Statistiques. Institute of Mathematical Statistics.
https://doi.org/10.1214/22-AIHP1333
chicago: Agresti, Antonio, and Mark Veraar. “Stochastic Maximal Lp(Lq)-Regularity
for Second Order Systems with Periodic Boundary Conditions.” Annales de l’Institut
Henri Poincaré, Probabilités et Statistiques. Institute of Mathematical Statistics,
2024. https://doi.org/10.1214/22-AIHP1333.
ieee: A. Agresti and M. Veraar, “Stochastic maximal Lp(Lq)-regularity for second
order systems with periodic boundary conditions,” Annales de l’Institut Henri
Poincaré, Probabilités et Statistiques, vol. 60, no. 1. Institute of Mathematical
Statistics, pp. 413–430, 2024.
ista: Agresti A, Veraar M. 2024. Stochastic maximal Lp(Lq)-regularity for second
order systems with periodic boundary conditions. Annales de l’Institut Henri Poincaré,
Probabilités et Statistiques. 60(1), 413–430.
mla: Agresti, Antonio, and Mark Veraar. “Stochastic Maximal Lp(Lq)-Regularity for
Second Order Systems with Periodic Boundary Conditions.” Annales de l’Institut
Henri Poincaré, Probabilités et Statistiques, vol. 60, no. 1, Institute of
Mathematical Statistics, 2024, pp. 413–30, doi:10.1214/22-AIHP1333.
short: A. Agresti, M. Veraar, Annales de l’Institut Henri Poincaré, Probabilités
et Statistiques 60 (2024) 413–430.
corr_author: '1'
das_tickbox: '0'
date_created: 2024-03-17T23:00:58Z
date_published: 2024-02-01T00:00:00Z
date_updated: 2026-10-15T09:46:19Z
day: '01'
department:
- _id: JuFi
doi: 10.1214/22-AIHP1333
external_id:
arxiv:
- '2106.01274'
fulldoi: https://doi.org/10.1214/22-AIHP1333
intvolume: ' 60'
issue: '1'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://doi.org/10.48550/arXiv.2106.01274
month: '02'
oa: 1
oa_version: Preprint
page: 413-430
publication: Annales de l'Institut Henri Poincaré, Probabilités et Statistiques
publication_identifier:
issn:
- 0246-0203
publication_status: published
publisher: Institute of Mathematical Statistics
quality_controlled: '1'
researchdata_availability: no
scopus_import: '1'
status: public
supplementarymaterial: no
title: Stochastic maximal Lp(Lq)-regularity for second order systems with periodic
boundary conditions
type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 60
year: '2024'
...