We study the Riemann problem for the multidimensional compressible isentropic Euler equations. Using the framework developed by Chiodaroli, De Lellis, Kreml and based on the techniques of De Lellis and Sz\'{ e}kelyhidi, we extend our previous results and prove that whenever the initial Riemann data give rise to a self-similar solution consisting of one admissible shock and one rarefaction wave and are not too far from lying on a simple shock wave, the problem admits also infinitely many admissible weak solutions.
Categories: math.AP