Seminar Analysis: Emil Wiedemann
Emil Wiedemann, Universität Leipzig
Existence of weak solutions to the incompressible Euler equations
The incompressible Euler equations form a system of nonlinear partial differential equations which describes the motion of an ideal fluid. Recently, C. De Lellis and L. Székelyhidi used a completely new approach to these equations involving convex integration and Baire category techniques in order to improve previous non-uniqueness results for weak solutions. After giving a brief overview of their work, I will present two global existence theorems that rely on it. In particular, I will discuss what role the kinetic energy plays in these existence results, and what can be said about the set of initial data for which non-unique solutions with non-increasing energy exist.