Well-posedness for a stochastic 2D Euler equation with transport noise

We prove the existence of a unique global strong solution for a stochastic two-dimensional Euler vorticity equation for incompressible flows with noise of transport type. In particular, we show that the initial smoothness of the solution is preserved. The arguments are based on approximating the sol...

Descripción completa

Detalles Bibliográficos
Autores principales: Lang, Oana, Crisan, Dan
Formato: Online Artículo Texto
Lenguaje:English
Publicado: Springer US 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10185632/
https://www.ncbi.nlm.nih.gov/pubmed/37205178
http://dx.doi.org/10.1007/s40072-021-00233-7
_version_ 1785042398390255616
author Lang, Oana
Crisan, Dan
author_facet Lang, Oana
Crisan, Dan
author_sort Lang, Oana
collection PubMed
description We prove the existence of a unique global strong solution for a stochastic two-dimensional Euler vorticity equation for incompressible flows with noise of transport type. In particular, we show that the initial smoothness of the solution is preserved. The arguments are based on approximating the solution of the Euler equation with a family of viscous solutions which is proved to be relatively compact using a tightness criterion by Kurtz.
format Online
Article
Text
id pubmed-10185632
institution National Center for Biotechnology Information
language English
publishDate 2022
publisher Springer US
record_format MEDLINE/PubMed
spelling pubmed-101856322023-05-17 Well-posedness for a stochastic 2D Euler equation with transport noise Lang, Oana Crisan, Dan Stoch Partial Differ Equ Article We prove the existence of a unique global strong solution for a stochastic two-dimensional Euler vorticity equation for incompressible flows with noise of transport type. In particular, we show that the initial smoothness of the solution is preserved. The arguments are based on approximating the solution of the Euler equation with a family of viscous solutions which is proved to be relatively compact using a tightness criterion by Kurtz. Springer US 2022-01-29 2023 /pmc/articles/PMC10185632/ /pubmed/37205178 http://dx.doi.org/10.1007/s40072-021-00233-7 Text en © The Author(s) 2022 https://creativecommons.org/licenses/by/4.0/Open AccessThis article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/ (https://creativecommons.org/licenses/by/4.0/) .
spellingShingle Article
Lang, Oana
Crisan, Dan
Well-posedness for a stochastic 2D Euler equation with transport noise
title Well-posedness for a stochastic 2D Euler equation with transport noise
title_full Well-posedness for a stochastic 2D Euler equation with transport noise
title_fullStr Well-posedness for a stochastic 2D Euler equation with transport noise
title_full_unstemmed Well-posedness for a stochastic 2D Euler equation with transport noise
title_short Well-posedness for a stochastic 2D Euler equation with transport noise
title_sort well-posedness for a stochastic 2d euler equation with transport noise
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC10185632/
https://www.ncbi.nlm.nih.gov/pubmed/37205178
http://dx.doi.org/10.1007/s40072-021-00233-7
work_keys_str_mv AT langoana wellposednessforastochastic2deulerequationwithtransportnoise
AT crisandan wellposednessforastochastic2deulerequationwithtransportnoise

Ejemplares similares