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Non-uniqueness of admissible weak solutions to the compressible Euler equations with smooth initial data Kreml, Ondřej


We consider the isentropic Euler equations of gas dynamics in the whole two-dimensional space and we prove the existence of a $C^\infty$ initial datum which admits infinitely many bounded admissible weak solutions. Taking advantage of the relation between smooth solutions to the Euler system and to the Burgers equation we construct a smooth compression wave which collapses into a perturbed Riemann state at some time instant $T > 0$. In order to continue the solution after the formation of the discontinuity, we adjust and apply the theory developed by De Lellis and Székelyhidi and we construct infinitely many solutions. </p>

This is a joint work with Elisabetta Chiodaroli, V\'aclav M\'acha and Sebastian Schwarzacher. </p>

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