Geodesic
A note on measure-valued solutions to the full Euler system
Applications of Mathematics, Tome 67 (2022) no. 4, pp. 419-430.

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We construct two particular solutions of the full Euler system which emanate from the same initial data. Our aim is to show that the convex combination of these two solutions form a measure-valued solution which may not be approximated by a sequence of weak solutions. As a result, the weak* closure of the set of all weak solutions, considered as parametrized measures, is not equal to the space of all measure-valued solutions. This is in stark contrast with the incompressible Euler equations.
DOI : 10.21136/AM.2021.0279-20
Classification : 35B99, 35Q31
Keywords: measure-valued solution; compressible Euler system 
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Mácha, Václav; Wiedemann, Emil. A note on measure-valued solutions to the full Euler system. Applications of Mathematics, Tome 67 (2022) no. 4, pp. 419-430. doi : 10.21136/AM.2021.0279-20. http://geodesic.mathdoc.fr/articles/10.21136/AM.2021.0279-20/

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