University of Heidelberg, Applied Analysis Seminar
Thu 06.05.2021
14:15, posted in Applied Analysis
Dr. Ibrokhimbek Akramov (Heidelberg University)
Non-Unique Admissible Weak Solutions of the Compressible Euler Equations with Compact Support in Space
Online via HeiCONF

In this talk, we will present the existence of compactly supported admissible solutions to the Cauchy problem for the isentropic compressible Euler equations. In more than one space dimension, convex integration techniques developed by De Lellis-Sz\'ekelyhidi and Chiodaroli enable us to prove failure of uniqueness on a finite time-interval for admissible solutions starting from any continuously differentiable initial density and suitably constructed bounded initial momenta. In particular, this extends Chiodaroli's work from periodic boundary conditions to bounded domains or the whole space.

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