---
_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.
date_created: 2023-06-18T22:00:45Z
date_published: 2023-09-25T00:00:00Z
date_updated: 2024-01-29T11:04:41Z
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
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creator: dernst
date_created: 2024-01-29T11:03:09Z
date_updated: 2024-01-29T11:03:09Z
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file_size: 834638
relation: main_file
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file_date_updated: 2024-01-29T11:03:09Z
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: '9240'
abstract:
- lang: eng
text: A stochastic PDE, describing mesoscopic fluctuations in systems of weakly
interacting inertial particles of finite volume, is proposed and analysed in any
finite dimension . It is a regularised and inertial version of the Dean–Kawasaki
model. A high-probability well-posedness theory for this model is developed. This
theory improves significantly on the spatial scaling restrictions imposed in an
earlier work of the same authors, which applied only to significantly larger particles
in one dimension. The well-posedness theory now applies in d-dimensions when the
particle-width ϵ is proportional to for and N is the number of particles. This
scaling is optimal in a certain Sobolev norm. Key tools of the analysis are fractional
Sobolev spaces, sharp bounds on Bessel functions, separability of the regularisation
in the d-spatial dimensions, and use of the Faà di Bruno's formula.
acknowledgement: All authors thank the anonymous referee for his/her careful reading
of the manuscript and valuable suggestions. This paper was motivated by stimulating
discussions at the First Berlin–Leipzig Workshop on Fluctuating Hydrodynamics in
August 2019 with Ana Djurdjevac, Rupert Klein and Ralf Kornhuber. JZ gratefully
acknowledges funding by a Royal Society Wolfson Research Merit Award. FC gratefully
acknowledges funding from the European Union’s Horizon 2020 research and innovation
programme under the Marie Skłodowska-Curie grant agreement No. 754411.
article_processing_charge: Yes (via OA deal)
article_type: original
author:
- first_name: Federico
full_name: Cornalba, Federico
id: 2CEB641C-A400-11E9-A717-D712E6697425
last_name: Cornalba
- first_name: Tony
full_name: Shardlow, Tony
last_name: Shardlow
- first_name: Johannes
full_name: Zimmer, Johannes
last_name: Zimmer
citation:
ama: Cornalba F, Shardlow T, Zimmer J. Well-posedness for a regularised inertial
Dean–Kawasaki model for slender particles in several space dimensions. Journal
of Differential Equations. 2021;284(5):253-283. doi:10.1016/j.jde.2021.02.048
apa: Cornalba, F., Shardlow, T., & Zimmer, J. (2021). Well-posedness for a regularised
inertial Dean–Kawasaki model for slender particles in several space dimensions.
Journal of Differential Equations. Elsevier. https://doi.org/10.1016/j.jde.2021.02.048
chicago: Cornalba, Federico, Tony Shardlow, and Johannes Zimmer. “Well-Posedness
for a Regularised Inertial Dean–Kawasaki Model for Slender Particles in Several
Space Dimensions.” Journal of Differential Equations. Elsevier, 2021. https://doi.org/10.1016/j.jde.2021.02.048.
ieee: F. Cornalba, T. Shardlow, and J. Zimmer, “Well-posedness for a regularised
inertial Dean–Kawasaki model for slender particles in several space dimensions,”
Journal of Differential Equations, vol. 284, no. 5. Elsevier, pp. 253–283,
2021.
ista: Cornalba F, Shardlow T, Zimmer J. 2021. Well-posedness for a regularised inertial
Dean–Kawasaki model for slender particles in several space dimensions. Journal
of Differential Equations. 284(5), 253–283.
mla: Cornalba, Federico, et al. “Well-Posedness for a Regularised Inertial Dean–Kawasaki
Model for Slender Particles in Several Space Dimensions.” Journal of Differential
Equations, vol. 284, no. 5, Elsevier, 2021, pp. 253–83, doi:10.1016/j.jde.2021.02.048.
short: F. Cornalba, T. Shardlow, J. Zimmer, Journal of Differential Equations 284
(2021) 253–283.
date_created: 2021-03-14T23:01:32Z
date_published: 2021-05-25T00:00:00Z
date_updated: 2023-08-07T14:08:05Z
day: '25'
ddc:
- '510'
department:
- _id: JuFi
doi: 10.1016/j.jde.2021.02.048
ec_funded: 1
external_id:
isi:
- '000634823300010'
file:
- access_level: open_access
checksum: c630b691fb9e716b02aa6103a9794ec8
content_type: application/pdf
creator: dernst
date_created: 2021-03-22T07:18:01Z
date_updated: 2021-03-22T07:18:01Z
file_id: '9267'
file_name: 2021_JourDiffEquations_Cornalba.pdf
file_size: 473310
relation: main_file
success: 1
file_date_updated: 2021-03-22T07:18:01Z
has_accepted_license: '1'
intvolume: ' 284'
isi: 1
issue: '5'
language:
- iso: eng
month: '05'
oa: 1
oa_version: Published Version
page: 253-283
project:
- _id: 260C2330-B435-11E9-9278-68D0E5697425
call_identifier: H2020
grant_number: '754411'
name: ISTplus - Postdoctoral Fellowships
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: Well-posedness for a regularised inertial Dean–Kawasaki model for slender particles
in several space dimensions
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: 284
year: '2021'
...