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}
}