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A note on measure-valued solutions to the full Euler system

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Abstract

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.

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Authors and Affiliations

  1. Institute of Mathematics of the Czech Academy of Sciences, Žitná 25, 115 67, Praha 1, Czech Republic

    Václav Mácha

  2. Ulm University, Institute of Applied Analysis, Helmholtzstr. 18, 89081, Ulm, Germany

    Emil Wiedemann

Authors
  1. Václav Mácha
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  2. Emil Wiedemann
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Corresponding author

Correspondence to Václav Mácha.

Additional information

The research of V. Mácha was supported by the Czech Science Foundation, Grant Agreement GA18-05974S, in the framework of RVO: 67985840.

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Mácha, V., Wiedemann, E. A note on measure-valued solutions to the full Euler system. Appl Math 67, 419–430 (2022). https://doi.org/10.21136/AM.2021.0279-20

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  • DOI: https://doi.org/10.21136/AM.2021.0279-20

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