---
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:
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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'
...
---
_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'
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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
license: https://creativecommons.org/licenses/by/4.0/
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'
...
---
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: '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
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creator: dernst
date_created: 2025-01-09T08:23:36Z
date_updated: 2025-01-09T08:23:36Z
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language:
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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'
...
---
_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'
...
---
_id: '12429'
abstract:
- lang: eng
text: In this paper, we consider traces at initial times for functions with mixed
time-space smoothness. Such results are often needed in the theory of evolution
equations. Our result extends and unifies many previous results. Our main improvement
is that we can allow general interpolation couples. The abstract results are applied
to regularity problems for fractional evolution equations and stochastic evolution
equations, where uniform trace estimates on the half-line are shown.
acknowledgement: The first author has been partially supported by the Nachwuchsring—Network
for the promotion of young scientists—at TU Kaiserslautern. The second and third
authors were supported by the Vidi subsidy 639.032.427 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: Nick
full_name: Lindemulder, Nick
last_name: Lindemulder
- first_name: Mark
full_name: Veraar, Mark
last_name: Veraar
citation:
ama: Agresti A, Lindemulder N, Veraar M. On the trace embedding and its applications
to evolution equations. Mathematische Nachrichten. 2023;296(4):1319-1350.
doi:10.1002/mana.202100192
apa: Agresti, A., Lindemulder, N., & Veraar, M. (2023). On the trace embedding
and its applications to evolution equations. Mathematische Nachrichten.
Wiley. https://doi.org/10.1002/mana.202100192
chicago: Agresti, Antonio, Nick Lindemulder, and Mark Veraar. “On the Trace Embedding
and Its Applications to Evolution Equations.” Mathematische Nachrichten.
Wiley, 2023. https://doi.org/10.1002/mana.202100192.
ieee: A. Agresti, N. Lindemulder, and M. Veraar, “On the trace embedding and its
applications to evolution equations,” Mathematische Nachrichten, vol. 296,
no. 4. Wiley, pp. 1319–1350, 2023.
ista: Agresti A, Lindemulder N, Veraar M. 2023. On the trace embedding and its applications
to evolution equations. Mathematische Nachrichten. 296(4), 1319–1350.
mla: Agresti, Antonio, et al. “On the Trace Embedding and Its Applications to Evolution
Equations.” Mathematische Nachrichten, vol. 296, no. 4, Wiley, 2023, pp.
1319–50, doi:10.1002/mana.202100192.
short: A. Agresti, N. Lindemulder, M. Veraar, Mathematische Nachrichten 296 (2023)
1319–1350.
date_created: 2023-01-29T23:00:59Z
date_published: 2023-04-01T00:00:00Z
date_updated: 2023-08-16T11:41:42Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1002/mana.202100192
external_id:
arxiv:
- '2104.05063'
isi:
- '000914134900001'
file:
- access_level: open_access
checksum: 6f099f1d064173784d1a27716a2cc795
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creator: dernst
date_created: 2023-08-16T11:40:02Z
date_updated: 2023-08-16T11:40:02Z
file_id: '14067'
file_name: 2023_MathNachrichten_Agresti.pdf
file_size: 449280
relation: main_file
success: 1
file_date_updated: 2023-08-16T11:40:02Z
fulldoi: https://doi.org/10.1002/mana.202100192
has_accepted_license: '1'
intvolume: ' 296'
isi: 1
issue: '4'
language:
- iso: eng
license: https://creativecommons.org/licenses/by-nc/4.0/
month: '04'
oa: 1
oa_version: Published Version
page: 1319-1350
publication: Mathematische Nachrichten
publication_identifier:
eissn:
- 1522-2616
issn:
- 0025-584X
publication_status: published
publisher: Wiley
quality_controlled: '1'
scopus_import: '1'
status: public
title: On the trace embedding and its applications to evolution equations
tmp:
image: /images/cc_by_nc.png
legal_code_url: https://creativecommons.org/licenses/by-nc/4.0/legalcode
name: Creative Commons Attribution-NonCommercial 4.0 International (CC BY-NC 4.0)
short: CC BY-NC (4.0)
type: journal_article
user_id: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 296
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
checksum: 246b703b091dfe047bfc79abf0891a63
content_type: application/pdf
creator: dernst
date_created: 2024-01-29T11:03:09Z
date_updated: 2024-01-29T11:03:09Z
file_id: '14895'
file_name: 2023_JourDifferentialEquations_Agresti.pdf
file_size: 834638
relation: main_file
success: 1
file_date_updated: 2024-01-29T11:03:09Z
fulldoi: https://doi.org/10.1016/j.jde.2023.05.038
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'
...
---
_id: '14772'
abstract:
- lang: eng
text: "Many coupled evolution equations can be described via 2×2-block operator
matrices of the form A=[ \r\nA\tB\r\nC\tD\r\n ] in a product space X=X1×X2 with
possibly unbounded entries. Here, the case of diagonally dominant block operator
matrices is considered, that is, the case where the full operator A can be seen
as a relatively bounded perturbation of its diagonal part with D(A)=D(A)×D(D)
though with possibly large relative bound. For such operators the properties of
sectoriality, R-sectoriality and the boundedness of the H∞-calculus are studied,
and for these properties perturbation results for possibly large but structured
perturbations are derived. Thereby, the time dependent parabolic problem associated
with A can be analyzed in maximal Lpt\r\n-regularity spaces, and this is applied
to a wide range of problems such as different theories for liquid crystals, an
artificial Stokes system, strongly damped wave and plate equations, and a Keller-Segel
model."
acknowledgement: "We would like to thank Tim Binz, Emiel Lorist and Mark Veraar for
valuable discussions. We also thank the anonymous referees for their helpful comments
and suggestions, and for the very accurate reading of the manuscript.\r\nThe first
author has been supported partially by the Nachwuchsring – Network for the promotion
of young scientists – at TU Kaiserslautern. Both authors have been supported by
MathApp – Mathematics Applied to Real-World Problems - part of the Research Initiative
of the Federal State of Rhineland-Palatinate, Germany."
article_number: '110146'
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: Amru
full_name: Hussein, Amru
last_name: Hussein
citation:
ama: Agresti A, Hussein A. Maximal Lp-regularity and H∞-calculus for block operator
matrices and applications. Journal of Functional Analysis. 2023;285(11).
doi:10.1016/j.jfa.2023.110146
apa: Agresti, A., & Hussein, A. (2023). Maximal Lp-regularity and H∞-calculus
for block operator matrices and applications. Journal of Functional Analysis.
Elsevier. https://doi.org/10.1016/j.jfa.2023.110146
chicago: Agresti, Antonio, and Amru Hussein. “Maximal Lp-Regularity and H∞-Calculus
for Block Operator Matrices and Applications.” Journal of Functional Analysis.
Elsevier, 2023. https://doi.org/10.1016/j.jfa.2023.110146.
ieee: A. Agresti and A. Hussein, “Maximal Lp-regularity and H∞-calculus for block
operator matrices and applications,” Journal of Functional Analysis, vol.
285, no. 11. Elsevier, 2023.
ista: Agresti A, Hussein A. 2023. Maximal Lp-regularity and H∞-calculus for block
operator matrices and applications. Journal of Functional Analysis. 285(11), 110146.
mla: Agresti, Antonio, and Amru Hussein. “Maximal Lp-Regularity and H∞-Calculus
for Block Operator Matrices and Applications.” Journal of Functional Analysis,
vol. 285, no. 11, 110146, Elsevier, 2023, doi:10.1016/j.jfa.2023.110146.
short: A. Agresti, A. Hussein, Journal of Functional Analysis 285 (2023).
corr_author: '1'
date_created: 2024-01-10T09:15:18Z
date_published: 2023-12-01T00:00:00Z
date_updated: 2024-10-09T21:07:48Z
day: '01'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1016/j.jfa.2023.110146
external_id:
arxiv:
- '2108.01962'
isi:
- '001081809000001'
file:
- access_level: open_access
checksum: eda98ca2aa73da91bd074baed34c2b3c
content_type: application/pdf
creator: dernst
date_created: 2024-01-10T11:23:57Z
date_updated: 2024-01-10T11:23:57Z
file_id: '14789'
file_name: 2023_JourFunctionalAnalysis_Agresti.pdf
file_size: 1120592
relation: main_file
success: 1
file_date_updated: 2024-01-10T11:23:57Z
fulldoi: https://doi.org/10.1016/j.jfa.2023.110146
has_accepted_license: '1'
intvolume: ' 285'
isi: 1
issue: '11'
keyword:
- Analysis
language:
- iso: eng
month: '12'
oa: 1
oa_version: Published Version
publication: Journal of Functional Analysis
publication_identifier:
issn:
- 0022-1236
publication_status: published
publisher: Elsevier
quality_controlled: '1'
scopus_import: '1'
status: public
title: Maximal Lp-regularity and H∞-calculus for block operator matrices and applications
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: 285
year: '2023'
...
---
_id: '11701'
abstract:
- lang: eng
text: In this paper we develop a new approach to nonlinear stochastic partial differential
equations with Gaussian noise. Our aim is to provide an abstract framework which
is applicable to a large class of SPDEs and includes many important cases of nonlinear
parabolic problems which are of quasi- or semilinear type. This first part is
on local existence and well-posedness. A second part in preparation is on blow-up
criteria and regularization. Our theory is formulated in an Lp-setting, and because
of this we can deal with nonlinearities in a very efficient way. Applications
to several concrete problems and their quasilinear variants are given. This includes
Burgers' equation, the Allen–Cahn equation, the Cahn–Hilliard equation, reaction–diffusion
equations, and the porous media equation. The interplay of the nonlinearities
and the critical spaces of initial data leads to new results and insights for
these SPDEs. The proofs are based on recent developments in maximal regularity
theory for the linearized problem for deterministic and stochastic evolution equations.
In particular, our theory can be seen as a stochastic version of the theory of
critical spaces due to Prüss–Simonett–Wilke (2018). Sharp weighted time-regularity
allow us to deal with rough initial values and obtain instantaneous regularization
results. The abstract well-posedness results are obtained by a combination of
several sophisticated splitting and truncation arguments.
acknowledgement: The second author is supported by the VIDI subsidy 639.032.427 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. Nonlinear parabolic stochastic evolution equations in
critical spaces Part I. Stochastic maximal regularity and local existence. Nonlinearity.
2022;35(8):4100-4210. doi:10.1088/1361-6544/abd613
apa: Agresti, A., & Veraar, M. (2022). Nonlinear parabolic stochastic evolution
equations in critical spaces Part I. Stochastic maximal regularity and local existence.
Nonlinearity. IOP Publishing. https://doi.org/10.1088/1361-6544/abd613
chicago: Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution
Equations in Critical Spaces Part I. Stochastic Maximal Regularity and Local Existence.”
Nonlinearity. IOP Publishing, 2022. https://doi.org/10.1088/1361-6544/abd613.
ieee: A. Agresti and M. Veraar, “Nonlinear parabolic stochastic evolution equations
in critical spaces Part I. Stochastic maximal regularity and local existence,”
Nonlinearity, vol. 35, no. 8. IOP Publishing, pp. 4100–4210, 2022.
ista: Agresti A, Veraar M. 2022. Nonlinear parabolic stochastic evolution equations
in critical spaces Part I. Stochastic maximal regularity and local existence.
Nonlinearity. 35(8), 4100–4210.
mla: Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution
Equations in Critical Spaces Part I. Stochastic Maximal Regularity and Local Existence.”
Nonlinearity, vol. 35, no. 8, IOP Publishing, 2022, pp. 4100–210, doi:10.1088/1361-6544/abd613.
short: A. Agresti, M. Veraar, Nonlinearity 35 (2022) 4100–4210.
date_created: 2022-07-31T22:01:47Z
date_published: 2022-08-04T00:00:00Z
date_updated: 2023-08-03T12:25:08Z
day: '04'
ddc:
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department:
- _id: JuFi
doi: 10.1088/1361-6544/abd613
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- '2001.00512'
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page: 4100-4210
publication: Nonlinearity
publication_identifier:
eissn:
- 1361-6544
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quality_controlled: '1'
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title: Nonlinear parabolic stochastic evolution equations in critical spaces Part
I. Stochastic maximal regularity and local existence
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---
_id: '11858'
abstract:
- lang: eng
text: "This paper is a continuation of Part I of this project, where we developed
a new local well-posedness theory for nonlinear stochastic PDEs with Gaussian
noise. In the current Part II we consider blow-up criteria and regularization
phenomena. As in Part I we can allow nonlinearities with polynomial growth and
rough initial values from critical spaces. In the first main result we obtain
several new blow-up criteria for quasi- and semilinear stochastic evolution equations.
In particular, for semilinear equations we obtain a Serrin type blow-up criterium,
which extends a recent result of Prüss–Simonett–Wilke (J Differ Equ 264(3):2028–2074,
2018) to the stochastic setting. Blow-up criteria can be used to prove global
well-posedness for SPDEs. As in Part I, maximal regularity techniques and weights
in time play a central role in the proofs. Our second contribution is a new method
to bootstrap Sobolev and Hölder regularity in time and space, which does not require
smoothness of the initial data. The blow-up criteria are at the basis of these
new methods. Moreover, in applications the bootstrap results can be combined with
our blow-up criteria, to obtain efficient ways to prove global existence. This
gives new results even in classical \U0001D43F2-settings, which we illustrate
for a concrete SPDE. In future works in preparation we apply the results of the
current paper to obtain global well-posedness results and regularity for several
concrete SPDEs. These include stochastic Navier–Stokes equations, reaction– diffusion
equations and the Allen–Cahn equation. Our setting allows to put these SPDEs into
a more flexible framework, where less restrictions on the nonlinearities are needed,
and we are able to treat rough initial values from critical spaces. Moreover,
we will obtain higher-order regularity results."
acknowledgement: "The authors thank Emiel Lorist for helpful comments. The authors
thank the anonymous referees for their helpful remarks to improve the presentation.\r\nOpen
access funding provided by Institute of Science and Technology (IST Austria)."
article_number: '56'
article_processing_charge: Yes (via OA deal)
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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. Nonlinear parabolic stochastic evolution equations in
critical spaces part II. Journal of Evolution Equations. 2022;22(2). doi:10.1007/s00028-022-00786-7
apa: Agresti, A., & Veraar, M. (2022). Nonlinear parabolic stochastic evolution
equations in critical spaces part II. Journal of Evolution Equations. Springer
Nature. https://doi.org/10.1007/s00028-022-00786-7
chicago: Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution
Equations in Critical Spaces Part II.” Journal of Evolution Equations.
Springer Nature, 2022. https://doi.org/10.1007/s00028-022-00786-7.
ieee: A. Agresti and M. Veraar, “Nonlinear parabolic stochastic evolution equations
in critical spaces part II,” Journal of Evolution Equations, vol. 22, no.
2. Springer Nature, 2022.
ista: Agresti A, Veraar M. 2022. Nonlinear parabolic stochastic evolution equations
in critical spaces part II. Journal of Evolution Equations. 22(2), 56.
mla: Agresti, Antonio, and Mark Veraar. “Nonlinear Parabolic Stochastic Evolution
Equations in Critical Spaces Part II.” Journal of Evolution Equations,
vol. 22, no. 2, 56, Springer Nature, 2022, doi:10.1007/s00028-022-00786-7.
short: A. Agresti, M. Veraar, Journal of Evolution Equations 22 (2022).
corr_author: '1'
date_created: 2022-08-16T08:39:43Z
date_published: 2022-06-01T00:00:00Z
date_updated: 2024-10-09T21:03:06Z
day: '01'
ddc:
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doi: 10.1007/s00028-022-00786-7
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fulldoi: https://doi.org/10.1007/s00028-022-00786-7
has_accepted_license: '1'
intvolume: ' 22'
isi: 1
issue: '2'
keyword:
- Mathematics (miscellaneous)
language:
- iso: eng
month: '06'
oa: 1
oa_version: Published Version
publication: Journal of Evolution Equations
publication_identifier:
eissn:
- 1424-3202
issn:
- 1424-3199
publication_status: published
publisher: Springer Nature
quality_controlled: '1'
scopus_import: '1'
status: public
title: Nonlinear parabolic stochastic evolution equations in critical spaces part
II
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legal_code_url: https://creativecommons.org/licenses/by/4.0/legalcode
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type: journal_article
user_id: 4359f0d1-fa6c-11eb-b949-802e58b17ae8
volume: 22
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...