A numerical glimpse at some non-standard solutions to compressible euler equations

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Abstract

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.

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Chiodaroli, E., & Gosse, L. (2017). A numerical glimpse at some non-standard solutions to compressible euler equations. Springer INdAM Series, 16, 111–140. https://doi.org/10.1007/978-3-319-49262-9_4

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