## 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

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BibTeX]

*Preprint*

**Inserted:** 10 nov 2015

**Last Updated:** 10 nov 2015

**Year:** 2015

**Abstract:**

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.

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