---
_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. <i>Stochastics and Partial Differential
    Equations: Analysis and Computations</i>. 2024;12:53-133. doi:<a href="https://doi.org/10.1007/s40072-022-00277-3">10.1007/s40072-022-00277-3</a>'
  apa: 'Agresti, A., Hieber, M., Hussein, A., &#38; Saal, M. (2024). The stochastic
    primitive equations with transport noise and turbulent pressure. <i>Stochastics
    and Partial Differential Equations: Analysis and Computations</i>. Springer Nature.
    <a href="https://doi.org/10.1007/s40072-022-00277-3">https://doi.org/10.1007/s40072-022-00277-3</a>'
  chicago: 'Agresti, Antonio, Matthias Hieber, Amru Hussein, and Martin Saal. “The
    Stochastic Primitive Equations with Transport Noise and Turbulent Pressure.” <i>Stochastics
    and Partial Differential Equations: Analysis and Computations</i>. Springer Nature,
    2024. <a href="https://doi.org/10.1007/s40072-022-00277-3">https://doi.org/10.1007/s40072-022-00277-3</a>.'
  ieee: 'A. Agresti, M. Hieber, A. Hussein, and M. Saal, “The stochastic primitive
    equations with transport noise and turbulent pressure,” <i>Stochastics and Partial
    Differential Equations: Analysis and Computations</i>, 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.” <i>Stochastics and Partial Differential Equations:
    Analysis and Computations</i>, vol. 12, Springer Nature, 2024, pp. 53–133, doi:<a
    href="https://doi.org/10.1007/s40072-022-00277-3">10.1007/s40072-022-00277-3</a>.'
  short: 'A. Agresti, M. Hieber, A. Hussein, M. Saal, Stochastics and Partial Differential
    Equations: Analysis and Computations 12 (2024) 53–133.'
date_created: 2023-01-12T12:12:29Z
date_published: 2024-03-01T00:00:00Z
date_updated: 2024-07-22T09:30:40Z
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
has_accepted_license: '1'
intvolume: '        12'
isi: 1
keyword:
- Applied Mathematics
- Modeling and Simulation
- Statistics and Probability
language:
- iso: eng
license: https://creativecommons.org/licenses/by/4.0/
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'
scopus_import: '1'
status: public
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: 2DF688A6-F248-11E8-B48F-1D18A9856A87
volume: 12
year: '2024'
...