# Non-uniqueness of admissible weak solutions to the Riemann problem for the isentropic Euler equations

## TL;DR

This paper demonstrates that for certain initial conditions in the multidimensional isentropic Euler equations, the Riemann problem admits infinitely many admissible weak solutions, highlighting non-uniqueness issues.

## Contribution

It extends previous results by showing non-uniqueness of solutions for a broader class of initial data using advanced convex integration techniques.

## Key findings

- Existence of infinitely many admissible weak solutions under specific initial conditions
- Non-uniqueness occurs near simple shock wave configurations
- Application of convex integration methods to multidimensional Euler equations

## Abstract

We study the Riemann problem for the multidimensional compressible isentropic Euler equations. Using the framework developed by Chiodaroli, De Lellis, Kreml and based on the techniques of De Lellis and Sz\'{e}kelyhidi, we extend our previous results and prove that whenever the initial Riemann data give rise to a self-similar solution consisting of one admissible shock and one rarefaction wave and are not too far from lying on a simple shock wave, the problem admits also infinitely many admissible weak solutions.