# On global-in-time weak solutions to the magnetohydrodynamic system of compressible inviscid fluids

## TL;DR

This paper demonstrates the ill-posedness of the initial value problem for the magnetohydrodynamic system of inviscid compressible fluids and heat-conductive fluids using convex integration methods, highlighting challenges in establishing weak solutions.

## Contribution

It extends convex integration techniques to the Euler system with variable coefficients, showing ill-posedness for a broad class of initial data in magnetohydrodynamics.

## Key findings

- The initial value problem is ill-posed for a large class of data.
- The same ill-posedness result applies to heat-conductive fluids under certain conditions.
- Convex integration can be adapted to systems with variable coefficients.

## Abstract

We consider the motion of an inviscid compressible fluid under the mutual interactions with magnetic field. We show that the initial value problem is ill--posed in the class of weak solutions for a large class of physically admissible data. We also consider the same problem for inviscid heat--conductive fluid and show the same result under certain restrictions imposed on the magnetic field. The main tool is the method of convex integration adapted to the Euler system with `variable coefficients'.