A Geometric View on Stochastic Euler Equations

Explore a geometric perspective on stochastic Euler equations in this 43-minute lecture from the Hausdorff Junior Trimester Program on Randomness, PDEs, and Nonlinear Fluctuations. Delve into the application of V. Arnold's trick to rewrite certain stochastic PDEs on compact manifolds as stochastic differential equations on infinite-dimensional manifolds. Discover how the Ebin and Marsden machinery, originally developed for deterministic cases, can be utilized to establish the existence and uniqueness of strong solutions in high-regularity Sobolev mapping spaces. Gain insights into a novel approach that combines stochastic analysis and infinite-dimensional geometry techniques to prove local well-posedness of stochastic non-linear partial differential equations. The lecture covers joint work with M. Maurelli and K. Modin, as detailed in arXiv:1909.09982.