A counterexample to well-posedness of entropy solutions to the   compressible Euler system
  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. 
Elisabetta Chiodaroli
math.AP