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

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. This is a joint work with Elisabetta Chiodaroli, V\'aclav M\'acha and Sebastian Schwarzacher. Non UBCUnreviewedAuthor affiliation: Czech Academy of SciencesOthe