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

How to construct the global smooth solutions to the compressible viscous, non-isentropic, 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 str...

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Bibliographic Details
Published in:The Journal of geometric analysis 2023-08, Vol.33 (8), Article 246
Main Authors: Li, Yongsheng, Xu, Huan, Zhai, Xiaoping
Format: Article
Language:English
Subjects:
Abstract Harmonic Analysis
Compressibility
Conducting fluids
Convex and Discrete Geometry
Decay rate
Differential Geometry
Dynamical Systems and Ergodic Theory
Fourier Analysis
Geometry
Global Analysis and Analysis on Manifolds
Magnetic diffusion
Magnetic fields
Magnetohydrodynamic equations
Magnetohydrodynamic flow
Mathematical analysis
Mathematics
Mathematics and Statistics
Nonlinear systems
Perturbation
Stability
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Summary:How to construct the global smooth solutions to the compressible viscous, non-isentropic, 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.
ISSN:1050-6926
1559-002X
DOI:10.1007/s12220-023-01304-y