Global Smooth Solutions to the 3D Compressible Viscous Non-Isentropic Magnetohydrodynamic Flows Without Magnetic Diffusion

摘要

How to construct the global smooth solutions to the compressible viscous, nonisentropic, non-resistive magnetohydrodynamic equations in T-3 appears to be unknown. In this paper, we give a positive answer to this problem. More precisely, we prove a global stability result on perturbations near a strong background magnetic field to the 3D compressible viscous, non-isentropic, non-resistive magnetohydrodynamic equations. This stability result provides a significant example of the stabilizing effect of the magnetic field on electrically conducting fluids. In addition, we obtain an explicit decay rate for the solutions to this nonlinear system.

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