Magnetic Stabilization of Compressible Flows: Global Existence in 3D Inviscid Non-Isentropic MHD Equations

TL;DR

This paper proves that magnetic fields can prevent finite-time singularities in 3D inviscid non-isentropic compressible MHD flows, ensuring global smooth solutions near a background magnetic field, aligning with physical observations.

Contribution

It establishes the first rigorous proof of global existence and stability of smooth solutions in 3D inviscid non-isentropic MHD equations with magnetic stabilization.

Findings

Finite-time blowup is ruled out for the studied equations.

Global smooth solutions exist near a background magnetic field.

Results confirm physical experiments on magnetic stabilization.

Abstract

Solutions to the compressible Euler equations in all dimensions have been shown to develop finite-time singularities from smooth initial data such as shocks and cusps. There is an extraordinary list of results on this subject. When the inviscid compressible flow is coupled with the magnetic field in the 3D inviscid non-isentropic compressible magnetohydrodynamic (MHD) equations in $\mathbb{T}^3$, this paper rules out finite-time blowup and establishes the global existence of smooth and stable solutions near a suitable background magnetic field. This result rigorously confirms the stabilizing phenomenon observed in physical experiments involving electrically conducting fluids.