The primitive equations with stochastic wind driven boundary conditions

Fuente: arXiv
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Main Authors: Binz, Tim, Hieber, Matthias, Hussein, Amru, Saal, Martin
Format: Preprint
Published: 2020
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_version_ 1866915173787238400
author Binz, Tim
Hieber, Matthias
Hussein, Amru
Saal, Martin
author_facet Binz, Tim
Hieber, Matthias
Hussein, Amru
Saal, Martin
contents The primitive equations for geophysical flows are studied under the influence of {\em stochastic wind driven boundary conditions} modeled by a cylindrical Wiener process. We adapt an approach by Da Prato and Zabczyk for stochastic boundary value problems to define a notion of solutions. Then a rigorous treatment of these stochastic boundary conditions, which combines stochastic and deterministic methods, yields that these equations admit a unique, local pathwise solution within the anisotropic $L^q_t$-$H^{-1,p}_zL^p_{xy}$-setting. This solution is constructed in critical spaces.
format Preprint
id arxiv_https___arxiv_org_abs_2009_09449
institution arXiv
publishDate 2020
record_format arxiv
spellingShingle The primitive equations with stochastic wind driven boundary conditions
Binz, Tim
Hieber, Matthias
Hussein, Amru
Saal, Martin
Probability
Analysis of PDEs
Primary: 35Q86, Secondary: 35R60, 60H15, 76D03, 76M35, 76U60, 35K61
The primitive equations for geophysical flows are studied under the influence of {\em stochastic wind driven boundary conditions} modeled by a cylindrical Wiener process. We adapt an approach by Da Prato and Zabczyk for stochastic boundary value problems to define a notion of solutions. Then a rigorous treatment of these stochastic boundary conditions, which combines stochastic and deterministic methods, yields that these equations admit a unique, local pathwise solution within the anisotropic $L^q_t$-$H^{-1,p}_zL^p_{xy}$-setting. This solution is constructed in critical spaces.
title The primitive equations with stochastic wind driven boundary conditions
topic Probability
Analysis of PDEs
Primary: 35Q86, Secondary: 35R60, 60H15, 76D03, 76M35, 76U60, 35K61
url https://arxiv.org/abs/2009.09449