On the density of "wild" initial data for the barotropic Euler system

TL;DR

This paper demonstrates that the set of initial data leading to infinitely many solutions in the barotropic Euler system is dense in the phase space, highlighting the system's complex solution structure.

Contribution

It proves the density of 'wild data' in the $L^p$-topology for the barotropic Euler system, revealing the prevalence of non-uniqueness in solutions.

Findings

'Wild data' are dense in the phase space.

Infinitely many admissible entropy solutions exist for dense initial data.

The result emphasizes the complexity of the Euler system's solution landscape.

Abstract

We show that the set of ``wild data'', meaning the initial data for which the barotropic Euler system admits infinitely many admissible entropy solutions, is dense in the $L^p-$topology of the phase space.