Algebra and Analysis Seminar: Weak solutions to the stationary Euler equations

Antoine Choffrut (University of Edinburgh)

Abstract:

I will present some recent results in collaboration with László Székelyhidi. We construct so-called "wild'' solutions to the stationary Euler equations analogous to what De Lellis and Székelyhidi did for the time-dependent case. Perhaps surprisingly so, the stationary case does not follow from the time-dependent case.

This type of results falls under the name of h-principle and the main technical tool is the method of convex integration. In this talk I will first explain precisely what an h-principle is and how convex integration works. Then, I will highlight the main difficulties of the stationary case. In technical terms, the relaxation set in 2D is strictly smaller than what one finds in the time-dependent case.