A Numerical Glimpse at Some Non-standard Solutions to Compressible Euler Equations

In this note we review and recast some recent results on the existence of non-standard solutions to the compressible Euler equations as to make possible a preliminary numerical investigation. In particular, we are interested in studying numerically the forward in time evolution of some Lipschitz initial data which allow for non-standard solutions ("colliding data"). Numerical results indicate appearance of oscillations after the first break-up time along with a qualitative behavior seemingly compatible with relevant properties of non-standard solutions.