Incompressible Euler equations with stochastic forcing: A geometric approach

Mario Maurelli, Klas Modin and Alexander Schmeding

Stochastic Processes and their Applications, 2023, vol. 159, issue C, 101-148

Abstract: We consider a stochastic version of Euler equations using the infinite-dimensional geometric approach as pioneered by Ebin and Marsden (1970). For the Euler equations on a compact manifold (possibly with smooth boundary) we establish local existence and uniqueness of a strong solution in spaces of Sobolev mappings (of high enough regularity). Our approach combines techniques from stochastic analysis and infinite-dimensional geometry and provides a novel toolbox to establish local well-posedness of stochastic non-linear partial differential equations.

Keywords: Stochastic Euler equation; half-Lie group; Manifold of Sobolev mappings; Ebin–Marsden theory; Stochastic integration on Hilbert manifolds (search for similar items in EconPapers)
Date: 2023
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Persistent link: https://EconPapers.repec.org/RePEc:eee:spapps:v:159:y:2023:i:c:p:101-148

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DOI: 10.1016/j.spa.2023.01.011

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