Non-uniqueness of admissible weak solutions to the Riemann problem for the isentropic Euler equations

摘要

We study the Riemann problem for the multidimensional compressible isentropicEuler equations. Using the framework developed by Chiodaroli, De Lellis, Kremland based on the techniques of De Lellis and Sz\'{e}kelyhidi, we extend ourprevious results and prove that whenever the initial Riemann data give rise toa self-similar solution consisting of one admissible shock and one rarefactionwave and are not too far from lying on a simple shock wave, the problem admitsalso infinitely many admissible weak solutions.