Non-uniqueness of admissible weak solutions to the two-dimensional barotropic compressible Euler system with contact discontinuities

TL;DR

This paper demonstrates that for specific initial conditions involving contact discontinuities, the two-dimensional barotropic compressible Euler system admits infinitely many admissible weak solutions, highlighting non-uniqueness in such scenarios.

Contribution

It introduces convex integration techniques to prove the existence of infinitely many solutions for the 2D Euler system with contact discontinuities, revealing non-uniqueness.

Findings

Existence of infinitely many admissible weak solutions for certain Riemann data.

Non-uniqueness of solutions in the presence of contact discontinuities.

Application of convex integration to 2D Euler system.

Abstract

This paper is concerned with the Riemann problem for the two-dimensional barotropic compressible Euler system with a general strictly increasing pressure law. By means of convex integration, the existence of infinitely many admissible weak solutions is established for certain Riemann initial data for which the corresponding one-dimensional self-similar solution consists solely of a contact discontinuity.