---
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:
- access_level: open_access
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
has_accepted_license: '1'
intvolume: ' 48'
issue: '2'
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
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: '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'
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: 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. 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, 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, 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, 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'
date_created: 2021-09-13T12:17:10Z
date_published: 2025-05-01T00:00:00Z
date_updated: 2025-05-28T09:27:05Z
day: '01'
department:
- _id: JuFi
doi: 10.4310/jdg/1747065796
ec_funded: 1
external_id:
arxiv:
- '2109.04233'
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
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: '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).
date_created: 2024-09-08T22:01:10Z
date_published: 2024-09-03T00:00:00Z
date_updated: 2025-09-08T09:11:41Z
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
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'
scopus_import: '1'
status: public
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.
date_created: 2023-02-02T10:45:15Z
date_published: 2024-04-01T00:00:00Z
date_updated: 2025-09-04T11:27:46Z
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
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'
scopus_import: '1'
status: public
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'
...
---
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'
date_created: 2023-02-02T10:45:47Z
date_published: 2024-09-01T00:00:00Z
date_updated: 2025-08-05T13:23:09Z
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
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'
scopus_import: '1'
status: public
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
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'
date_created: 2024-01-14T23:00:57Z
date_published: 2024-10-01T00:00:00Z
date_updated: 2025-09-04T11:43:43Z
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
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'
scopus_import: '1'
status: public
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'
...
---
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.
date_created: 2024-03-10T23:00:54Z
date_published: 2024-10-01T00:00:00Z
date_updated: 2025-09-04T12:19:59Z
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
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'
scopus_import: '1'
status: public
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'
...
---
_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).
date_created: 2024-04-21T22:00:52Z
date_published: 2024-05-01T00:00:00Z
date_updated: 2025-09-04T13:45:40Z
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
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'
scopus_import: '1'
status: public
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'
...
---
_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'
date_created: 2024-08-04T22:01:21Z
date_published: 2024-08-01T00:00:00Z
date_updated: 2025-09-08T08:46:57Z
day: '01'
department:
- _id: JuFi
doi: 10.1137/23M1562482
ec_funded: 1
external_id:
arxiv:
- '2301.06897'
isi:
- '001315424500021'
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'
scopus_import: '1'
status: public
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'
...
---
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'
date_created: 2024-08-25T22:01:08Z
date_published: 2024-09-01T00:00:00Z
date_updated: 2025-09-08T09:01:00Z
day: '01'
department:
- _id: JuFi
doi: 10.1137/23M1603819
ec_funded: 1
external_id:
arxiv:
- '2309.06798'
isi:
- '001285416500001'
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'
scopus_import: '1'
status: public
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: '17481'
abstract:
- lang: eng
text: "Phase-field models such as the Allen–Cahn equation may give rise to the formation
and evolution of geometric shapes, a phenomenon that may be analyzed rigorously
in suitable scaling regimes. In its sharp-interface limit, the vectorial Allen–Cahn
equation with a potential with N≥3 distinct minima has been conjectured to describe
the evolution of branched interfaces by multiphase mean curvature flow. In the
present work, we give a rigorous proof for this statement in two and three ambient
dimensions and for a suitable class of potentials: as long as a strong solution
to multiphase mean curvature flow exists, solutions to the vectorial Allen–Cahn
equation with well-prepared initial data converge towards multiphase mean curvature
flow in the limit of vanishing interface width parameter ε↘0. We even establish
the rate of convergence O(ε \r\n1/2\r\n ). Our approach is based on the gradient-flow
structure of the Allen–Cahn equation and its limiting motion: building on the
recent concept of “gradient-flow calibrations” for multiphase mean curvature flow,
we introduce a notion of relative entropy for the vectorial Allen–Cahn equation
with multi-well potential. This enables us to overcome the limitations of other
approaches, e.g. avoiding the need for a stability analysis of the Allen–Cahn
operator or additional convergence hypotheses for the energy at positive times."
acknowledgement: "The authors thank Sebastian Hensel for useful and helpful commentson
the first draft of this work.\r\nThis project has received funding from the European
Research Council (ERC)\r\nunder the European Union’s Horizon 2020 research and innovation
programme (grant\r\nagreement no. 948819."
article_processing_charge: Yes
article_type: original
author:
- 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: Alice
full_name: Marveggio, Alice
id: 25647992-AA84-11E9-9D75-8427E6697425
last_name: Marveggio
citation:
ama: Fischer JL, Marveggio A. Quantitative convergence of the vectorial Allen–Cahn
equation towards multiphase mean curvature flow. Annales de l’Institut Henri
Poincare C. 2024;41(5):1117-1178. doi:10.4171/AIHPC/109
apa: Fischer, J. L., & Marveggio, A. (2024). Quantitative convergence of the
vectorial Allen–Cahn equation towards multiphase mean curvature flow. Annales
de l’Institut Henri Poincare C. EMS Press. https://doi.org/10.4171/AIHPC/109
chicago: Fischer, Julian L, and Alice Marveggio. “Quantitative Convergence of the
Vectorial Allen–Cahn Equation towards Multiphase Mean Curvature Flow.” Annales
de l’Institut Henri Poincare C. EMS Press, 2024. https://doi.org/10.4171/AIHPC/109.
ieee: J. L. Fischer and A. Marveggio, “Quantitative convergence of the vectorial
Allen–Cahn equation towards multiphase mean curvature flow,” Annales de l’Institut
Henri Poincare C, vol. 41, no. 5. EMS Press, pp. 1117–1178, 2024.
ista: Fischer JL, Marveggio A. 2024. Quantitative convergence of the vectorial Allen–Cahn
equation towards multiphase mean curvature flow. Annales de l’Institut Henri Poincare
C. 41(5), 1117–1178.
mla: Fischer, Julian L., and Alice Marveggio. “Quantitative Convergence of the Vectorial
Allen–Cahn Equation towards Multiphase Mean Curvature Flow.” Annales de l’Institut
Henri Poincare C, vol. 41, no. 5, EMS Press, 2024, pp. 1117–78, doi:10.4171/AIHPC/109.
short: J.L. Fischer, A. Marveggio, Annales de l’Institut Henri Poincare C 41 (2024)
1117–1178.
corr_author: '1'
date_created: 2024-09-01T22:01:09Z
date_published: 2024-01-24T00:00:00Z
date_updated: 2025-09-08T09:11:01Z
day: '24'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.4171/AIHPC/109
ec_funded: 1
external_id:
isi:
- '001293853900003'
file:
- access_level: open_access
checksum: b5ad02d9abd5b4701269cd1ad0a1cc8f
content_type: application/pdf
creator: dernst
date_created: 2024-09-09T07:46:42Z
date_updated: 2024-09-09T07:46:42Z
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oa: 1
oa_version: Published Version
page: 1117-1178
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call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Annales de l'Institut Henri Poincare C
publication_identifier:
eissn:
- 1873-1430
issn:
- 0294-1449
publication_status: published
publisher: EMS Press
quality_controlled: '1'
related_material:
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scopus_import: '1'
status: public
title: Quantitative convergence of the vectorial Allen–Cahn equation towards multiphase
mean curvature flow
tmp:
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type: journal_article
user_id: 317138e5-6ab7-11ef-aa6d-ffef3953e345
volume: 41
year: '2024'
...
---
_id: '13043'
abstract:
- lang: eng
text: "We derive a weak-strong uniqueness principle for BV solutions to multiphase
mean curvature flow of triple line clusters in three dimensions. Our proof is
based on the explicit construction\r\nof a gradient flow calibration in the sense
of the recent work of Fischer et al. (2020) for any such\r\ncluster. This extends
the two-dimensional construction to the three-dimensional case of surfaces\r\nmeeting
along triple junctions."
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.
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. Weak-strong uniqueness for the mean curvature flow of double
bubbles. Interfaces and Free Boundaries. 2023;25(1):37-107. doi:10.4171/IFB/484
apa: Hensel, S., & Laux, T. (2023). Weak-strong uniqueness for the mean curvature
flow of double bubbles. Interfaces and Free Boundaries. EMS Press. https://doi.org/10.4171/IFB/484
chicago: Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature
Flow of Double Bubbles.” Interfaces and Free Boundaries. EMS Press, 2023.
https://doi.org/10.4171/IFB/484.
ieee: S. Hensel and T. Laux, “Weak-strong uniqueness for the mean curvature flow
of double bubbles,” Interfaces and Free Boundaries, vol. 25, no. 1. EMS
Press, pp. 37–107, 2023.
ista: Hensel S, Laux T. 2023. Weak-strong uniqueness for the mean curvature flow
of double bubbles. Interfaces and Free Boundaries. 25(1), 37–107.
mla: Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature
Flow of Double Bubbles.” Interfaces and Free Boundaries, vol. 25, no. 1,
EMS Press, 2023, pp. 37–107, doi:10.4171/IFB/484.
short: S. Hensel, T. Laux, Interfaces and Free Boundaries 25 (2023) 37–107.
corr_author: '1'
date_created: 2023-05-21T22:01:06Z
date_published: 2023-04-20T00:00:00Z
date_updated: 2025-04-14T09:35:57Z
day: '20'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.4171/IFB/484
ec_funded: 1
external_id:
arxiv:
- '2108.01733'
isi:
- '000975817300002'
file:
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file_size: 867876
relation: main_file
success: 1
file_date_updated: 2023-05-22T07:24:13Z
has_accepted_license: '1'
intvolume: ' 25'
isi: 1
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language:
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month: '04'
oa: 1
oa_version: Published Version
page: 37-107
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Interfaces and Free Boundaries
publication_identifier:
eissn:
- 1463-9971
issn:
- 1463-9963
publication_status: published
publisher: EMS Press
quality_controlled: '1'
related_material:
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status: public
title: Weak-strong uniqueness for the mean curvature flow of double bubbles
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name: Creative Commons Attribution 4.0 International Public License (CC-BY 4.0)
short: CC BY (4.0)
type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 25
year: '2023'
...
---
_id: '13135'
abstract:
- lang: eng
text: In this paper we consider a class of stochastic reaction-diffusion equations.
We provide local well-posedness, regularity, blow-up criteria and positivity of
solutions. The key novelties of this work are related to the use transport noise,
critical spaces and the proof of higher order regularity of solutions – even in
case of non-smooth initial data. Crucial tools are Lp(Lp)-theory, maximal regularity
estimates and sharp blow-up criteria. We view the results of this paper as a general
toolbox for establishing global well-posedness for a large class of reaction-diffusion
systems of practical interest, of which many are completely open. In our follow-up
work [8], the results of this paper are applied in the specific cases of the Lotka-Volterra
equations and the Brusselator model.
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) Image 1. 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
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: Local well-posedness and positivity. Journal
of Differential Equations. 2023;368(9):247-300. doi:10.1016/j.jde.2023.05.038'
apa: 'Agresti, A., & Veraar, M. (2023). Reaction-diffusion equations with transport
noise and critical superlinear diffusion: Local well-posedness and positivity.
Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2023.05.038'
chicago: 'Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with
Transport Noise and Critical Superlinear Diffusion: Local Well-Posedness and Positivity.”
Journal of Differential Equations. Elsevier, 2023. https://doi.org/10.1016/j.jde.2023.05.038.'
ieee: 'A. Agresti and M. Veraar, “Reaction-diffusion equations with transport noise
and critical superlinear diffusion: Local well-posedness and positivity,” Journal
of Differential Equations, vol. 368, no. 9. Elsevier, pp. 247–300, 2023.'
ista: 'Agresti A, Veraar M. 2023. Reaction-diffusion equations with transport noise
and critical superlinear diffusion: Local well-posedness and positivity. Journal
of Differential Equations. 368(9), 247–300.'
mla: 'Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with Transport
Noise and Critical Superlinear Diffusion: Local Well-Posedness and Positivity.”
Journal of Differential Equations, vol. 368, no. 9, Elsevier, 2023, pp.
247–300, doi:10.1016/j.jde.2023.05.038.'
short: A. Agresti, M. Veraar, Journal of Differential Equations 368 (2023) 247–300.
corr_author: '1'
date_created: 2023-06-18T22:00:45Z
date_published: 2023-09-25T00:00:00Z
date_updated: 2025-04-14T07:53:59Z
day: '25'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1016/j.jde.2023.05.038
ec_funded: 1
external_id:
isi:
- '001019018700001'
file:
- access_level: open_access
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date_created: 2024-01-29T11:03:09Z
date_updated: 2024-01-29T11:03:09Z
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file_name: 2023_JourDifferentialEquations_Agresti.pdf
file_size: 834638
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has_accepted_license: '1'
intvolume: ' 368'
isi: 1
issue: '9'
language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: 247-300
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Journal of Differential Equations
publication_identifier:
eissn:
- 1090-2732
issn:
- 0022-0396
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: 'Reaction-diffusion equations with transport noise and critical superlinear
diffusion: Local well-posedness and positivity'
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: 368
year: '2023'
...
---
OA_place: publisher
_id: '14587'
abstract:
- lang: eng
text: "This thesis concerns the application of variational methods to the study
of evolution problems arising in fluid mechanics and in material sciences. The
main focus is on weak-strong stability properties of some curvature driven interface
evolution problems, such as the two-phase Navier–Stokes flow with surface tension
and multiphase mean curvature flow, and on the phase-field approximation of the
latter. Furthermore, we discuss a variational approach to the study of a class
of doubly nonlinear wave equations.\r\nFirst, we consider the two-phase Navier–Stokes
flow with surface tension within a bounded domain. The two fluids are immiscible
and separated by a sharp interface, which intersects the boundary of the domain
at a constant contact angle of ninety degree. We devise a suitable concept of
varifolds solutions for the associated interface evolution problem and we establish
a weak-strong uniqueness principle in case of a two dimensional ambient space.
In order to focus on the boundary effects and on the singular geometry of the
evolving domains, we work for simplicity in the regime of same viscosities for
the two fluids.\r\nThe core of the thesis consists in the rigorous proof of the
convergence of the vectorial Allen-Cahn equation towards multiphase mean curvature
flow for a suitable class of multi- well potentials and for well-prepared initial
data. We even establish a rate of convergence. Our relative energy approach relies
on the concept of gradient-flow calibration for branching singularities in multiphase
mean curvature flow and thus enables us to overcome the limitations of other approaches.
To the best of the author’s knowledge, our result is the first quantitative and
unconditional one available in the literature for the vectorial/multiphase setting.\r\nThis
thesis also contains a first study of weak-strong stability for planar multiphase
mean curvature flow beyond the singularity resulting from a topology change. Previous
weak-strong results are indeed limited to time horizons before the first topology
change of the strong solution. We consider circular topology changes and we prove
weak-strong stability for BV solutions to planar multiphase mean curvature flow
beyond the associated singular times by dynamically adapting the strong solutions
to the weak one by means of a space-time shift.\r\nIn the context of interface
evolution problems, our proofs for the main results of this thesis are based on
the relative energy technique, relying on novel suitable notions of relative energy
functionals, which in particular measure the interface error. Our statements follow
from the resulting stability estimates for the relative energy associated to the
problem.\r\nAt last, we introduce a variational approach to the study of nonlinear
evolution problems. This approach hinges on the minimization of a parameter dependent
family of convex functionals over entire trajectories, known as Weighted Inertia-Dissipation-Energy
(WIDE) functionals. We consider a class of doubly nonlinear wave equations and
establish the convergence, up to subsequences, of the associated WIDE minimizers
to a solution of the target problem as the parameter goes to zero."
acknowledgement: The research projects contained in this thesis have received funding
from the European Research Council (ERC) under the European Union’s Horizon 2020
research and innovation programme (grant agreement No 948819).
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Alice
full_name: Marveggio, Alice
id: 25647992-AA84-11E9-9D75-8427E6697425
last_name: Marveggio
citation:
ama: Marveggio A. Weak-strong stability and phase-field approximation of interface
evolution problems in fluid mechanics and in material sciences. 2023. doi:10.15479/at:ista:14587
apa: Marveggio, A. (2023). Weak-strong stability and phase-field approximation
of interface evolution problems in fluid mechanics and in material sciences.
Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:14587
chicago: Marveggio, Alice. “Weak-Strong Stability and Phase-Field Approximation
of Interface Evolution Problems in Fluid Mechanics and in Material Sciences.”
Institute of Science and Technology Austria, 2023. https://doi.org/10.15479/at:ista:14587.
ieee: A. Marveggio, “Weak-strong stability and phase-field approximation of interface
evolution problems in fluid mechanics and in material sciences,” Institute of
Science and Technology Austria, 2023.
ista: Marveggio A. 2023. Weak-strong stability and phase-field approximation of
interface evolution problems in fluid mechanics and in material sciences. Institute
of Science and Technology Austria.
mla: Marveggio, Alice. Weak-Strong Stability and Phase-Field Approximation of
Interface Evolution Problems in Fluid Mechanics and in Material Sciences.
Institute of Science and Technology Austria, 2023, doi:10.15479/at:ista:14587.
short: A. Marveggio, Weak-Strong Stability and Phase-Field Approximation of Interface
Evolution Problems in Fluid Mechanics and in Material Sciences, Institute of Science
and Technology Austria, 2023.
corr_author: '1'
date_created: 2023-11-21T11:41:05Z
date_published: 2023-11-21T00:00:00Z
date_updated: 2026-04-07T13:28:13Z
day: '21'
ddc:
- '515'
degree_awarded: PhD
department:
- _id: GradSch
- _id: JuFi
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call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication_identifier:
issn:
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publisher: Institute of Science and Technology Austria
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supervisor:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
title: Weak-strong stability and phase-field approximation of interface evolution
problems in fluid mechanics and in material sciences
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BY-NC-SA 4.0)
short: CC BY-NC-SA (4.0)
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2023'
...
---
_id: '12079'
abstract:
- lang: eng
text: We extend the recent rigorous convergence result of Abels and Moser (SIAM
J Math Anal 54(1):114–172, 2022. https://doi.org/10.1137/21M1424925) concerning
convergence rates for solutions of the Allen–Cahn equation with a nonlinear Robin
boundary condition towards evolution by mean curvature flow with constant contact
angle. More precisely, in the present work we manage to remove the perturbative
assumption on the contact angle being close to 90∘. We establish under usual double-well
type assumptions on the potential and for a certain class of boundary energy densities
the sub-optimal convergence rate of order ε12 for general contact angles α∈(0,π).
For a very specific form of the boundary energy density, we even obtain from our
methods a sharp convergence rate of order ε; again for general contact angles
α∈(0,π). Our proof deviates from the popular strategy based on rigorous asymptotic
expansions and stability estimates for the linearized Allen–Cahn operator. Instead,
we follow the recent approach by Fischer et al. (SIAM J Math Anal 52(6):6222–6233,
2020. https://doi.org/10.1137/20M1322182), thus relying on a relative entropy
technique. We develop a careful adaptation of their approach in order to encode
the constant contact angle condition. In fact, we perform this task at the level
of the notion of gradient flow calibrations. This concept was recently introduced
in the context of weak-strong uniqueness for multiphase mean curvature flow by
Fischer et al. (arXiv:2003.05478v2).
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.\r\nOpen
Access funding enabled and organized by Projekt DEAL."
article_number: '201'
article_processing_charge: No
article_type: original
author:
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
- first_name: Maximilian
full_name: Moser, Maximilian
id: a60047a9-da77-11eb-85b4-c4dc385ebb8c
last_name: Moser
citation:
ama: 'Hensel S, Moser M. Convergence rates for the Allen–Cahn equation with boundary
contact energy: The non-perturbative regime. Calculus of Variations and Partial
Differential Equations. 2022;61(6). doi:10.1007/s00526-022-02307-3'
apa: 'Hensel, S., & Moser, M. (2022). Convergence rates for the Allen–Cahn equation
with boundary contact energy: The non-perturbative regime. Calculus of Variations
and Partial Differential Equations. Springer Nature. https://doi.org/10.1007/s00526-022-02307-3'
chicago: 'Hensel, Sebastian, and Maximilian Moser. “Convergence Rates for the Allen–Cahn
Equation with Boundary Contact Energy: The Non-Perturbative Regime.” Calculus
of Variations and Partial Differential Equations. Springer Nature, 2022. https://doi.org/10.1007/s00526-022-02307-3.'
ieee: 'S. Hensel and M. Moser, “Convergence rates for the Allen–Cahn equation with
boundary contact energy: The non-perturbative regime,” Calculus of Variations
and Partial Differential Equations, vol. 61, no. 6. Springer Nature, 2022.'
ista: 'Hensel S, Moser M. 2022. Convergence rates for the Allen–Cahn equation with
boundary contact energy: The non-perturbative regime. Calculus of Variations and
Partial Differential Equations. 61(6), 201.'
mla: 'Hensel, Sebastian, and Maximilian Moser. “Convergence Rates for the Allen–Cahn
Equation with Boundary Contact Energy: The Non-Perturbative Regime.” Calculus
of Variations and Partial Differential Equations, vol. 61, no. 6, 201, Springer
Nature, 2022, doi:10.1007/s00526-022-02307-3.'
short: S. Hensel, M. Moser, Calculus of Variations and Partial Differential Equations
61 (2022).
date_created: 2022-09-11T22:01:54Z
date_published: 2022-08-24T00:00:00Z
date_updated: 2025-04-14T07:53:59Z
day: '24'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00526-022-02307-3
ec_funded: 1
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isi:
- '000844247300008'
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month: '08'
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'
scopus_import: '1'
status: public
title: 'Convergence rates for the Allen–Cahn equation with boundary contact energy:
The non-perturbative regime'
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volume: 61
year: '2022'
...
---
_id: '11842'
abstract:
- lang: eng
text: We consider the flow of two viscous and incompressible fluids within a bounded
domain modeled by means of a two-phase Navier–Stokes system. The two fluids are
assumed to be immiscible, meaning that they are separated by an interface. With
respect to the motion of the interface, we consider pure transport by the fluid
flow. Along the boundary of the domain, a complete slip boundary condition for
the fluid velocities and a constant ninety degree contact angle condition for
the interface are assumed. In the present work, we devise for the resulting evolution
problem a suitable weak solution concept based on the framework of varifolds and
establish as the main result a weak-strong uniqueness principle in 2D. The proof
is based on a relative entropy argument and requires a non-trivial further development
of ideas from the recent work of Fischer and the first author (Arch. Ration. Mech.
Anal. 236, 2020) to incorporate the contact angle condition. To focus on the effects
of the necessarily singular geometry of the evolving fluid domains, we work for
simplicity in the regime of same viscosities for the two fluids.
acknowledgement: The authors warmly thank their former resp. current PhD advisor Julian
Fischer for the suggestion of this problem and for valuable initial discussions
on the subjects of this paper. 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.
article_number: '93'
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: Alice
full_name: Marveggio, Alice
id: 25647992-AA84-11E9-9D75-8427E6697425
last_name: Marveggio
citation:
ama: Hensel S, Marveggio A. Weak-strong uniqueness for the Navier–Stokes equation
for two fluids with ninety degree contact angle and same viscosities. Journal
of Mathematical Fluid Mechanics. 2022;24(3). doi:10.1007/s00021-022-00722-2
apa: Hensel, S., & Marveggio, A. (2022). Weak-strong uniqueness for the Navier–Stokes
equation for two fluids with ninety degree contact angle and same viscosities.
Journal of Mathematical Fluid Mechanics. Springer Nature. https://doi.org/10.1007/s00021-022-00722-2
chicago: Hensel, Sebastian, and Alice Marveggio. “Weak-Strong Uniqueness for the
Navier–Stokes Equation for Two Fluids with Ninety Degree Contact Angle and Same
Viscosities.” Journal of Mathematical Fluid Mechanics. Springer Nature,
2022. https://doi.org/10.1007/s00021-022-00722-2.
ieee: S. Hensel and A. Marveggio, “Weak-strong uniqueness for the Navier–Stokes
equation for two fluids with ninety degree contact angle and same viscosities,”
Journal of Mathematical Fluid Mechanics, vol. 24, no. 3. Springer Nature,
2022.
ista: Hensel S, Marveggio A. 2022. Weak-strong uniqueness for the Navier–Stokes
equation for two fluids with ninety degree contact angle and same viscosities.
Journal of Mathematical Fluid Mechanics. 24(3), 93.
mla: Hensel, Sebastian, and Alice Marveggio. “Weak-Strong Uniqueness for the Navier–Stokes
Equation for Two Fluids with Ninety Degree Contact Angle and Same Viscosities.”
Journal of Mathematical Fluid Mechanics, vol. 24, no. 3, 93, Springer Nature,
2022, doi:10.1007/s00021-022-00722-2.
short: S. Hensel, A. Marveggio, Journal of Mathematical Fluid Mechanics 24 (2022).
corr_author: '1'
date_created: 2022-08-14T22:01:45Z
date_published: 2022-08-01T00:00:00Z
date_updated: 2026-04-07T13:28:13Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1007/s00021-022-00722-2
ec_funded: 1
external_id:
arxiv:
- '2112.11154'
isi:
- '000834834300001'
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creator: cchlebak
date_created: 2022-08-16T06:55:22Z
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intvolume: ' 24'
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- iso: eng
month: '08'
oa: 1
oa_version: Published Version
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call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: Journal of Mathematical Fluid Mechanics
publication_identifier:
eissn:
- 1422-6952
issn:
- 1422-6928
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
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relation: dissertation_contains
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scopus_import: '1'
status: public
title: Weak-strong uniqueness for the Navier–Stokes equation for two fluids with ninety
degree contact angle and same viscosities
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: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 24
year: '2022'
...
---
_id: '14597'
abstract:
- lang: eng
text: "Phase-field models such as the Allen-Cahn equation may give rise to the formation
and evolution of geometric shapes, a phenomenon that may be analyzed rigorously
in suitable scaling regimes. In its sharp-interface limit, the vectorial Allen-Cahn
equation with a potential with N≥3 distinct minima has been conjectured to describe
the evolution of branched interfaces by multiphase mean curvature flow.\r\nIn
the present work, we give a rigorous proof for this statement in two and three
ambient dimensions and for a suitable class of potentials: As long as a strong
solution to multiphase mean curvature flow exists, solutions to the vectorial
Allen-Cahn equation with well-prepared initial data converge towards multiphase
mean curvature flow in the limit of vanishing interface width parameter ε↘0. We
even establish the rate of convergence O(ε1/2).\r\nOur approach is based on the
gradient flow structure of the Allen-Cahn equation and its limiting motion: Building
on the recent concept of \"gradient flow calibrations\" for multiphase mean curvature
flow, we introduce a notion of relative entropy for the vectorial Allen-Cahn equation
with multi-well potential. This enables us to overcome the limitations of other
approaches, e.g. avoiding the need for a stability analysis of the Allen-Cahn
operator or additional convergence hypotheses for the energy at positive times."
article_number: '2203.17143'
article_processing_charge: No
arxiv: 1
author:
- 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: Alice
full_name: Marveggio, Alice
id: 25647992-AA84-11E9-9D75-8427E6697425
last_name: Marveggio
citation:
ama: Fischer JL, Marveggio A. Quantitative convergence of the vectorial Allen-Cahn
equation towards multiphase mean curvature flow. arXiv. doi:10.48550/ARXIV.2203.17143
apa: Fischer, J. L., & Marveggio, A. (n.d.). Quantitative convergence of the
vectorial Allen-Cahn equation towards multiphase mean curvature flow. arXiv.
https://doi.org/10.48550/ARXIV.2203.17143
chicago: Fischer, Julian L, and Alice Marveggio. “Quantitative Convergence of the
Vectorial Allen-Cahn Equation towards Multiphase Mean Curvature Flow.” ArXiv,
n.d. https://doi.org/10.48550/ARXIV.2203.17143.
ieee: J. L. Fischer and A. Marveggio, “Quantitative convergence of the vectorial
Allen-Cahn equation towards multiphase mean curvature flow,” arXiv. .
ista: Fischer JL, Marveggio A. Quantitative convergence of the vectorial Allen-Cahn
equation towards multiphase mean curvature flow. arXiv, 2203.17143.
mla: Fischer, Julian L., and Alice Marveggio. “Quantitative Convergence of the Vectorial
Allen-Cahn Equation towards Multiphase Mean Curvature Flow.” ArXiv, 2203.17143,
doi:10.48550/ARXIV.2203.17143.
short: J.L. Fischer, A. Marveggio, ArXiv (n.d.).
corr_author: '1'
date_created: 2023-11-23T09:30:02Z
date_published: 2022-03-31T00:00:00Z
date_updated: 2026-04-07T13:28:13Z
day: '31'
department:
- _id: JuFi
doi: 10.48550/ARXIV.2203.17143
ec_funded: 1
external_id:
arxiv:
- '2203.17143'
language:
- iso: eng
main_file_link:
- open_access: '1'
url: https://arxiv.org/abs/2203.17143
month: '03'
oa: 1
oa_version: Preprint
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: arXiv
publication_status: draft
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status: public
title: Quantitative convergence of the vectorial Allen-Cahn equation towards multiphase
mean curvature flow
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
year: '2022'
...
---
OA_place: publisher
_id: '10007'
abstract:
- lang: eng
text: The present thesis is concerned with the derivation of weak-strong uniqueness
principles for curvature driven interface evolution problems not satisfying a
comparison principle. The specific examples being treated are two-phase Navier-Stokes
flow with surface tension, modeling the evolution of two incompressible, viscous
and immiscible fluids separated by a sharp interface, and multiphase mean curvature
flow, which serves as an idealized model for the motion of grain boundaries in
an annealing polycrystalline material. Our main results - obtained in joint works
with Julian Fischer, Tim Laux and Theresa M. Simon - state that prior to the formation
of geometric singularities due to topology changes, the weak solution concept
of Abels (Interfaces Free Bound. 9, 2007) to two-phase Navier-Stokes flow with
surface tension and the weak solution concept of Laux and Otto (Calc. Var. Partial
Differential Equations 55, 2016) to multiphase mean curvature flow (for networks
in R^2 or double bubbles in R^3) represents the unique solution to these interface
evolution problems within the class of classical solutions, respectively. To the
best of the author's knowledge, for interface evolution problems not admitting
a geometric comparison principle the derivation of a weak-strong uniqueness principle
represented an open problem, so that the works contained in the present thesis
constitute the first positive results in this direction. The key ingredient of
our approach consists of the introduction of a novel concept of relative entropies
for a class of curvature driven interface evolution problems, for which the associated
energy contains an interfacial contribution being proportional to the surface
area of the evolving (network of) interface(s). The interfacial part of the relative
entropy gives sufficient control on the interface error between a weak and a classical
solution, and its time evolution can be computed, at least in principle, for any
energy dissipating weak solution concept. A resulting stability estimate for the
relative entropy essentially entails the above mentioned weak-strong uniqueness
principles. The present thesis contains a detailed introduction to our relative
entropy approach, which in particular highlights potential applications to other
problems in curvature driven interface evolution not treated in this thesis.
alternative_title:
- ISTA Thesis
article_processing_charge: No
author:
- first_name: Sebastian
full_name: Hensel, Sebastian
id: 4D23B7DA-F248-11E8-B48F-1D18A9856A87
last_name: Hensel
orcid: 0000-0001-7252-8072
citation:
ama: 'Hensel S. Curvature driven interface evolution: Uniqueness properties of weak
solution concepts. 2021. doi:10.15479/at:ista:10007'
apa: 'Hensel, S. (2021). Curvature driven interface evolution: Uniqueness properties
of weak solution concepts. Institute of Science and Technology Austria. https://doi.org/10.15479/at:ista:10007'
chicago: 'Hensel, Sebastian. “Curvature Driven Interface Evolution: Uniqueness Properties
of Weak Solution Concepts.” Institute of Science and Technology Austria, 2021.
https://doi.org/10.15479/at:ista:10007.'
ieee: 'S. Hensel, “Curvature driven interface evolution: Uniqueness properties of
weak solution concepts,” Institute of Science and Technology Austria, 2021.'
ista: 'Hensel S. 2021. Curvature driven interface evolution: Uniqueness properties
of weak solution concepts. Institute of Science and Technology Austria.'
mla: 'Hensel, Sebastian. Curvature Driven Interface Evolution: Uniqueness Properties
of Weak Solution Concepts. Institute of Science and Technology Austria, 2021,
doi:10.15479/at:ista:10007.'
short: 'S. Hensel, Curvature Driven Interface Evolution: Uniqueness Properties of
Weak Solution Concepts, Institute of Science and Technology Austria, 2021.'
corr_author: '1'
date_created: 2021-09-13T11:12:34Z
date_published: 2021-09-14T00:00:00Z
date_updated: 2026-04-08T07:01:01Z
day: '14'
ddc:
- '515'
degree_awarded: PhD
department:
- _id: GradSch
- _id: JuFi
doi: 10.15479/at:ista:10007
ec_funded: 1
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language:
- iso: eng
month: '09'
oa: 1
oa_version: Published Version
page: '300'
project:
- _id: 2564DBCA-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '665385'
name: International IST Doctoral Program
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication_identifier:
issn:
- 2663-337X
publication_status: published
publisher: Institute of Science and Technology Austria
related_material:
record:
- id: '10012'
relation: part_of_dissertation
status: public
- id: '10013'
relation: part_of_dissertation
status: public
- id: '7489'
relation: part_of_dissertation
status: public
status: public
supervisor:
- first_name: Julian L
full_name: Fischer, Julian L
id: 2C12A0B0-F248-11E8-B48F-1D18A9856A87
last_name: Fischer
orcid: 0000-0002-0479-558X
title: 'Curvature driven interface evolution: Uniqueness properties of weak solution
concepts'
type: dissertation
user_id: ba8df636-2132-11f1-aed0-ed93e2281fdd
year: '2021'
...
---
_id: '10013'
abstract:
- lang: eng
text: We derive a weak-strong uniqueness principle for BV solutions to multiphase
mean curvature flow of triple line clusters in three dimensions. Our proof is
based on the explicit construction of a gradient-flow calibration in the sense
of the recent work of Fischer et al. [arXiv:2003.05478] for any such cluster.
This extends the two-dimensional construction to the three-dimensional case of
surfaces meeting along triple junctions.
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.
article_number: '2108.01733'
article_processing_charge: No
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. Weak-strong uniqueness for the mean curvature flow of double
bubbles. arXiv. doi:10.48550/arXiv.2108.01733
apa: Hensel, S., & Laux, T. (n.d.). Weak-strong uniqueness for the mean curvature
flow of double bubbles. arXiv. https://doi.org/10.48550/arXiv.2108.01733
chicago: Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature
Flow of Double Bubbles.” ArXiv, n.d. https://doi.org/10.48550/arXiv.2108.01733.
ieee: S. Hensel and T. Laux, “Weak-strong uniqueness for the mean curvature flow
of double bubbles,” arXiv. .
ista: Hensel S, Laux T. Weak-strong uniqueness for the mean curvature flow of double
bubbles. arXiv, 2108.01733.
mla: Hensel, Sebastian, and Tim Laux. “Weak-Strong Uniqueness for the Mean Curvature
Flow of Double Bubbles.” ArXiv, 2108.01733, doi:10.48550/arXiv.2108.01733.
short: S. Hensel, T. Laux, ArXiv (n.d.).
corr_author: '1'
date_created: 2021-09-13T12:17:11Z
date_published: 2021-08-03T00:00:00Z
date_updated: 2026-04-08T07:01:01Z
day: '03'
department:
- _id: JuFi
doi: 10.48550/arXiv.2108.01733
ec_funded: 1
external_id:
arxiv:
- '2108.01733'
language:
- iso: eng
main_file_link:
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url: https://arxiv.org/abs/2108.01733
month: '08'
oa: 1
oa_version: Preprint
project:
- _id: 0aa76401-070f-11eb-9043-b5bb049fa26d
call_identifier: H2020
grant_number: '948819'
name: Bridging Scales in Random Materials
publication: arXiv
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title: Weak-strong uniqueness for the mean curvature flow of double bubbles
type: preprint
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
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...