---
_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. <i>Journal
    of Differential Equations</i>. 2023;368(9):247-300. doi:<a href="https://doi.org/10.1016/j.jde.2023.05.038">10.1016/j.jde.2023.05.038</a>'
  apa: 'Agresti, A., &#38; Veraar, M. (2023). Reaction-diffusion equations with transport
    noise and critical superlinear diffusion: Local well-posedness and positivity.
    <i>Journal of Differential Equations</i>. Elsevier. <a href="https://doi.org/10.1016/j.jde.2023.05.038">https://doi.org/10.1016/j.jde.2023.05.038</a>'
  chicago: 'Agresti, Antonio, and Mark Veraar. “Reaction-Diffusion Equations with
    Transport Noise and Critical Superlinear Diffusion: Local Well-Posedness and Positivity.”
    <i>Journal of Differential Equations</i>. Elsevier, 2023. <a href="https://doi.org/10.1016/j.jde.2023.05.038">https://doi.org/10.1016/j.jde.2023.05.038</a>.'
  ieee: 'A. Agresti and M. Veraar, “Reaction-diffusion equations with transport noise
    and critical superlinear diffusion: Local well-posedness and positivity,” <i>Journal
    of Differential Equations</i>, 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.”
    <i>Journal of Differential Equations</i>, vol. 368, no. 9, Elsevier, 2023, pp.
    247–300, doi:<a href="https://doi.org/10.1016/j.jde.2023.05.038">10.1016/j.jde.2023.05.038</a>.'
  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
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  file_size: 834638
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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'
...