English

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

Analysis of PDEs 2020-01-08 v1

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'.

Keywords

Cite

@article{arxiv.1903.02039,
  title  = {On global-in-time weak solutions to the magnetohydrodynamic system of compressible inviscid fluids},
  author = {Eduard Feireisl and Yang Li},
  journal= {arXiv preprint arXiv:1903.02039},
  year   = {2020}
}