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Glimm's method and density of wild data for the Euler system of gas dynamics*

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Published 24 January 2024 • © 2024 IOP Publishing Ltd & London Mathematical Society
, , Citation Elisabetta Chiodaroli and Eduard Feireisl 2024 Nonlinearity 37 035005 DOI 10.1088/1361-6544/ad1cbd

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elisabetta.chiodaroli@unipi.it

Author affiliations

1 Dipartimento di Matematica, Università di Pisa, Largo Bruno Pontecorvo 5, Pisa, Italy

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

Author notes

3 The work of E F was partially supported by the Czech Sciences Foundation (GAČR), Grant Agreement 21–02411S. The Institute of Mathematics of the Academy of Sciences of the Czech Republic is supported by RVO:67985840.

4 Author to whom any correspondence should be addressed.

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Dates

  1. Received 26 June 2023
  2. Accepted 9 January 2024
  3. Published

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0951-7715/37/3/035005

Abstract

We adapt Glimm's approximation method to the framework of convex integration to show density of wild data for the (complete) Euler system of gas dynamics. The desired infinite family of entropy admissible solutions emanating from the same initial data is obtained via convex integration of suitable Riemann problems pasted with local smooth solutions. In addition, the wild data belong to BV class.

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10.1088/1361-6544/ad1cbd