# On the density of wild initial data for the compressible Euler system

## TL;DR

This paper investigates the set of initial data for the compressible Euler equations that lead to multiple weak solutions, showing that the class of such data is dense but not typical in the $L^1$ sense.

## Contribution

It characterizes the closure of wild initial data for the Euler system and demonstrates that the complement of this class is large and dense in the $L^1$ topology.

## Key findings

- The class of wild initial data is dense in the $L^1$ topology.
- The complement of this class is open and dense.
- Many initial data do not lead to multiple solutions, indicating typical well-posedness.

## Abstract

We consider a class of wild initial data to the compressible Euler system that give rise to infinitely many admissible weak solutions via the method of convex integration. We identify the closure of this class in the natural $L^1$-topology and show that its complement is rather large, specifically it is an open dense set.