Uniqueness of rarefaction waves in multidimensional compressible Euler   system
  We show that 1-D rarefaction wave solutions are unique in the class of bounded entropy solutions to the multidimensional compressible Euler system. Such a result may be viewed as a counterpart of the recent examples of non-uniqueness of the shock wave solutions to the Riemann problem, where infinitely many solutions are constructed by the method of convex integration. 
Eduard Feireisl, Ond\v{r}ej Kreml
math.AP