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

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'.

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Cited by in corpus (3)

• Global well-posedness to three-dimensional full compressible magnetohydrodynamic equations with vacuum
• Global well-posedness for the three-dimensional full compressible viscous non-resistive MHD system
• Entropy-bounded solutions to the 3D compressible heat-conducting magnetohydrodynamic equations with vacuum at infinity