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A note on the long-time behavior of dissipative solutions to the Euler system

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Abstract

We show that the Reynolds defect measure for a dissipative weak solution of the compressible Euler system vanishes for large time. This may be seen as a piece of evidence that the dissipative solutions are asymptotically close to weak solutions in the turbulent regime, whence suitable for describing compressible fluid flows in the long run.

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Authors and Affiliations

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

    Eduard Feireisl

  2. Institute of Mathematics, Technische Universität Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Eduard Feireisl

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  1. Eduard Feireisl
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Correspondence to Eduard Feireisl.

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Dedicated to Matthias Hieber on the occasion of his 60-th birthday.

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The research of E.F. leading to these results has received funding from the Czech Sciences Foundation (GAČR), Grant Agreement 18-05974S. The Institute of Mathematics of the Academy of Sciences of the Czech Republic is supported by RVO:67985840.

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Feireisl, E. A note on the long-time behavior of dissipative solutions to the Euler system. J. Evol. Equ. 21, 2807–2814 (2021). https://doi.org/10.1007/s00028-021-00696-0

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  • DOI: https://doi.org/10.1007/s00028-021-00696-0

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