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...

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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
Descripción
Sumario: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.

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