Special Session 23: Recent progress in the mathematical theory of compressible fluid flows
Contents
We analyze the Riemann problem for the compressible isentropic Euler system in the whole space $\mathbb{R}^2$. Using the tools developed by De Lellis and Sz\'{e}kelyhidi for the incompressible Euler system we show that for every Riemann initial data yielding the self-similar solution in the form of two admissible shocks there exist in fact infinitely many admissible bounded weak solutions. Moreover for some of these initial data such solutions dissipate more total energy than the self-similar solution which might be looked at as a natural candidate for the "physical" solution.