A-free rigidity and applications to the compressible Euler system

0476952 - MÚ 2018 RIV DE eng J - Journal Article
Chiodaroli, E. - Feireisl, Eduard - Kreml, Ondřej - Wiedemann, E.
A-free rigidity and applications to the compressible Euler system.
Annali di Matematica Pura ed Applicata. Roč. 196, č. 4 (2017), s. 1557-1572. ISSN 0373-3114. E-ISSN 1618-1891
R&D Projects: GA ČR GA13-00522S
EU Projects: European Commission(XE) 320078 - MATHEF
Institutional support: RVO:67985840
Keywords : A-free condition * compressible Euler equations * measure-valued solutions
OECD category: Pure mathematics
Impact factor: 1.066, year: 2017
https://link.springer.com/article/10.1007%2Fs10231-016-0629-9

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.
Permanent Link: http://hdl.handle.net/11104/0273355