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Carnegie Mellon NSF logoCenter for Nonlinear Analysis
Emil Wiedemann
Afilliation: Hausdorff Center for Mathematics, Universitšt 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