A-free rigidity and applications to the compressible Euler system

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 cannot 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 Muller. While a priori it is not unexpected that not every measure-valued solution arises from a sequence of weak solutions, it is noteworthy that this observation in the compressible case is in contrast to the incompressible situation, where every measure-valued solution can be approximated by weak solutions, as shown by Szekelyhidi and Wiedemann.


Published in:
Annali Di Matematica Pura Ed Applicata, 196, 4, 1557-1572
Year:
2017
Publisher:
Heidelberg, Springer Verlag
ISSN:
0373-3114
Keywords:
Laboratories:




 Record created 2017-09-05, last modified 2018-09-13


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