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arXiv · 2311.08197

The Ebin-Marsden toolbox for stochastic PDEs: stochastic Euler equations

Zdzisław Brzeźniak·Mario Maurelli·Alexander Schmeding
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Abstract

The Ebin-Marsden theory is a powerful geometric framework for many PDEs from fluid dynamics. In this paper we provide a toolbox to apply the Ebin-Marsden approach to stochastic PDEs, combining tools from infinite-dimensional geometry and stochastic analysis. We showcase our approach in the context of incompressible Euler equation for an ideal fluid with additive noise. Among our main results there are: (i) local well-posedness of maximal solutions by using the Ebin-Marsden framework; (ii) a stochastic version of the celebrated no-loss-no-gain theorem.

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Zdzisław Brzeźniak, Mario Maurelli, Alexander Schmeding. 2023-11-14. The Ebin-Marsden toolbox for stochastic PDEs: stochastic Euler equations. https://arxiv.org/abs/2311.08197

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