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arXiv · 2009.09449

The primitive equations with stochastic wind driven boundary conditions

Tim Binz·Matthias Hieber·Amru Hussein·Martin Saal
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Abstract

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.

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Tim Binz, Matthias Hieber, Amru Hussein, Martin Saal. 2020-09-20. The primitive equations with stochastic wind driven boundary conditions. https://doi.org/10.1016/j.matpur.2024.01.001

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