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

2012/01/17 by Elisabetta Chiodaroli · 1 citation
Mathematics · #math.AP

paper · pdf · doi:10.1142/s0219891614500143

29 pages

arxiv created 2012/01/17 · arxiv updated 2014/08/26

Abstract

We deal with entropy solutions to the Cauchy problem for the isentropic compressible Euler equations in the space-periodic case. In more than one space dimension, the methods developed by De Lellis-Székelyhidi enable us to show 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.

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