Calculus of Variations and Geometric Measure Theory

E. Chiodaroli - E. Feireisl - O. Kreml - E. Wiedemann

A-free Rigidity and Applications to the Compressible Euler System

created by chiodaroli on 10 Nov 2015



Inserted: 10 nov 2015
Last Updated: 10 nov 2015

Year: 2015


Can every measure-valued solution to the compressible Euler equations be approximated by a sequence of weak solutions? We prove that the answer is negative: Generalizing a well-known rigidity result of Ball and James to a more general situation, we construct an explicit measure-valued solution for the compressible Euler equations which can not be generated by a sequence of distributional solutions. We also give an abstract necessary condition for measure-valued solutions to be generated by weak solutions, relying on work of Fonseca and Müller. This difference between weak and measure-valued solutions in the compressible case is in contrast with the incompressible situation, where every measure-valued solution can be approximated by weak solutions, as shown by Székelyhidi and Wiedemann.