Alexander Schmeding (NTNU, Trondheim)
Abstract:
Due to an idea by V. Arnold, certain partial differential equations (PDE) can be rewritten as ordinary differential equations (ODE) on infinite-dimensional manifolds.
One of the most prominent examples for this method is the Euler equation of an incompressible fluid. Ebin and Marsden have used this approach to establish local well-posedness of the Euler equations in their seminal 1970 annals of mathematics article.
In this talk we will present the main ideas of the Ebin-Marsden method in a non-technical way. We shall only hint at the technical challenges and instead focus on the main ideas.
Then we shall outline how these ideas can be used to establish a solution theory for stochastic PDE from fluid dynamics.
No specialized knowledge is necessary to follow this introductory talk to the subject. it is based on recent joint work with Z. Brzezniak (York), M. Maurelli (Pisa) and K. Modin (Gothenburg)
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