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A counterexample to well-posedness of entropy solutions to the compressible Euler system

Elisabetta Chiodaroli

École Polytechnique Fédérale de Lausanne, Bâtiment des Mathématiques, Station 8, CH-1015 Lausanne, Switzerland

https://doi.org/10.1142/S0219891614500143Cited by:80 (Source: Crossref)

Abstract

We consider entropy solutions to the Cauchy problem for the isentropic compressible Euler equations in the spatially periodic case. In more than one space dimension, the methods developed by De Lellis–Székelyhidi enable us to show here failure of uniqueness on a finite time-interval for entropy solutions starting from any continuously differentiable initial density and suitably constructed bounded initial linear momenta.

Keywords:

AMSC: 35L65, 35D05, 76N15

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