**Emil Wiedemann**

**Afilliation:**Hausdorff Center for Mathematics, Universität Bonn, Germany

**Title:**Weak and measure-valued solutions of the incompressible Euler equations

**Abstract:**Recently, De Lellis and Szekelyhidi used convex integration and Baire category methods to construct non-unique weak solutions for the incompressible Euler equations, thus in particular recovering celebrated results of Scheffer and Shnirelman. In my talk I wish to present two further consequences of their approach which I recently obtained (the second one jointly with L. Szekelyhidi): 1. A global existence and non-uniqueness result for weak solutions with bounded energy for arbitrary initial data; 2. A result concerning the relation between weak and measure-valued solutions in the sense of DiPerna and Majda; More precisely, we show that any measure-valued solution can be generated by a sequence of weak solutions.

**Slides:**WiedemannEmil.pdf