06 Okt 2021
14:15  - 16:00

via Zoom

Seminar Analysis and Mathematical Physics: Emil Wiedemann (Universität Ulm)

Measure-Valued Solutions for the Compressible Euler Equations

The concept of measure-valued solution was introduced to the theory of hyperbolic conservation laws by DiPerna in the 1980s. For nonlinear systems of hyperbolic type, such as the Euler equations of ideal fluids, measure-valued solutions are often the only available notion of solution, as the existence of 'honest' solutions is still unknown. Although this relaxation of the solution concept seems like a vast generalization, where a lot of infomation is lost, it turned out in work of Székelyhidi-W. (2012) that every measure-valued solution can be approximated by weak ones in the incompressible situation. For compressible flows, however, the situation is much different. I will discuss recent progress in this direction in joint work with Dennis Gallenmüller.

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