The Ebin-Marsden toolbox for stochastic PDEs: stochastic Euler equations
Probability
2023-12-08 v2 Analysis of PDEs
Differential Geometry
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.
Cite
@article{arxiv.2311.08197,
title = {The Ebin-Marsden toolbox for stochastic PDEs: stochastic Euler equations},
author = {Zdzisław Brzeźniak and Mario Maurelli and Alexander Schmeding},
journal= {arXiv preprint arXiv:2311.08197},
year = {2023}
}
Comments
85 pages, v2: Improved introduction and corrected minor mistakes, main results remain unchanged