Near a generic background magnetic field, small perturbations of the 3D inviscid non-isentropic compressible MHD system on the torus exist globally and decay, unlike the compressible Euler case.
Alexakis, Two-dimensional behavior of three-dimensional magnetohydrodynamic flow with a strong guiding field, Phys
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Magnetic Stabilization of Compressible Flows: Global Existence in 3D Inviscid Non-Isentropic MHD Equations
Near a generic background magnetic field, small perturbations of the 3D inviscid non-isentropic compressible MHD system on the torus exist globally and decay, unlike the compressible Euler case.