A -free rigidity and applications to the compressible Euler system

Chiodaroli E, Feireisl E, Kreml O, Wiedemann E (2017)

Publication Type: Journal article

Publication year: 2017

Journal

Annali Di Matematica Pura Ed Applicata Springer Verlag (Germany)

Book Volume: 196

Pages Range: 1557-1572

Journal Issue: 4

DOI: 10.1007/s10231-016-0629-9

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 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 Müller. 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 Székelyhidi and Wiedemann.

Authors with CRIS profile

Emil Wiedemann

Involved external institutions

École Polytechnique Fédérale de Lausanne (EPFL) CH Switzerland (CH) Academy of Sciences of the Czech Republic (ASCR) / Akademie věd České republiky (AVČR) CZ Czech Republic (CZ) Gottfried Wilhelm Leibniz Universität Hannover DE Germany (DE)

How to cite

APA:

Chiodaroli, E., Feireisl, E., Kreml, O., & Wiedemann, E. (2017). A -free rigidity and applications to the compressible Euler system. Annali Di Matematica Pura Ed Applicata, 196(4), 1557-1572. https://dx.doi.org/10.1007/s10231-016-0629-9

MLA:

Chiodaroli, Elisabetta, et al. "A -free rigidity and applications to the compressible Euler system." Annali Di Matematica Pura Ed Applicata 196.4 (2017): 1557-1572.

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