# Ill posedness for the full Euler system driven by multiplicative white noise

## TL;DR

This paper investigates the ill-posedness of the compressible Euler equations under multiplicative white noise, showing that for many initial conditions, infinitely many weak solutions exist that adhere to entropy criteria.

## Contribution

It identifies a broad class of initial data leading to ill-posedness in the stochastic Euler system, highlighting the non-uniqueness of solutions under noise.

## Key findings

- Existence of infinitely many solutions for certain initial data
- Solutions are adapted to the noise and entropy admissible
- Ill-posedness persists in the stochastic setting

## Abstract

We consider the Euler system describing the motion of a compressible fluid driven by a multiplicative white noise. We identify a large class of initial data for which the problem is ill posed - there exist infinitely many global in time weak solutions. The solutions are adapted to the noise and satisfy the entropy admissibility criterion.