Stochastic Euler equations: a geometric approach

Stochastic Euler equations: a geometric approach

Mario Maurelli, Università degli Studi di Milano

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In their celebrated work [Ann. Math. 1970], Ebin and Marsden have shown local well-posedness of the incompressible Euler equations in any dimension by solving a smooth ODE on the infinite-dimensional space of volume-preserving Sobolev diffeomorphisms.

In this talk, we will develop this approach for the incompressible Euler equations driven by an additive, stochastic force term: we will solve a stochastic ODE with smooth coefficients on the space of volume-preserving Sobolev diffeomorphisms and get in turn local well-posedness of the stochastic Euler equations. This approach is quite flexible and we believe it can be used for other stochastic PDEs.

Based on the work arXiv:1909.09982 , joint work with Klas Modin and Alexander Schmeding.