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

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.

29 pages

References in corpus (2)

• Existence of Weak Solutions for the Incompressible Euler Equations
• Maximal dissipation and well-posedness for the compressible Euler system

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