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

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

2012-01-17

arxiv.org/abs/1201.3470v1

Mathematics

Analysis of PDEs

29 pages

Scientific paper

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-Sz\'ekelyhidi 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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