Paper

(S)-convergence and approximation of oscillatory solutions in fluid dynamics

Published 17 February 2021 • © 2021 IOP Publishing Ltd & London Mathematical Society
, , Citation Eduard Feireisl 2021 Nonlinearity 34 2327 DOI 10.1088/1361-6544/abbd84

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feireisl@math.cas.cz

Author affiliations

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

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

Author notes

3 The work of EF was partially supported by 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.

Dates

  1. Received 13 June 2020
  2. Revised 3 September 2020
  3. Accepted 1 October 2020
  4. Published

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0951-7715/34/4/2327

Abstract

We propose a new concept of (S)-convergence applicable to numerical methods as well as other consistent approximations of the Euler system in gas dynamics. (S)-convergence, based on averaging in the spirit of the strong law of large numbers, reflects the asymptotic properties of a given approximate sequence better than the standard description via Young measures. Similarity with the tools of ergodic theory is discussed.

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10.1088/1361-6544/abbd84