Global existence of 3D MHD equations with mixed partial dissipation and magnetic diffusion

2013 ◽  
Vol 14 (1) ◽  
pp. 526-535 ◽  
Author(s):  
Fan Wang ◽  
Keyan Wang
Keyword(s):  
Global Existence ◽  
Mhd Equations ◽  
Magnetic Diffusion ◽  
Partial Dissipation

scholarly journals Stability of the 3D incompressible MHD equations with horizontal dissipation in periodic domain

2021 ◽  
Vol 6 (11) ◽  
pp. 11837-11849
Author(s):  
Ruihong Ji ◽  
◽  
Ling Tian ◽  
Keyword(s):  
Magnetic Field ◽  
Stability Problem ◽  
Stability Result ◽  
Mhd Equations ◽  
Periodic Domain ◽  
Magnetic Diffusion ◽  
Partial Dissipation ◽  
Background Magnetic Field ◽  
The Stability ◽  
Incompressible Mhd

<abstract><p>The stability problem on the magnetohydrodynamics (MHD) equations with partial or no dissipation is not well-understood. This paper focuses on the 3D incompressible MHD equations with mixed partial dissipation and magnetic diffusion. Our main result assesses the stability of perturbations near the steady solution given by a background magnetic field in periodic domain. The new stability result presented here is among few stability conclusions currently available for ideal or partially dissipated MHD equations.</p></abstract>

scholarly journals Global existence and decay of smooth solution for the 2-D MHD equations without magnetic diffusion

2014 ◽  
Vol 267 (2) ◽  
pp. 503-541 ◽  
Author(s):  
Xiaoxia Ren ◽  
Jiahong Wu ◽  
Zhaoyin Xiang ◽  
Zhifei Zhang
Keyword(s):  
Global Existence ◽  
Smooth Solution ◽  
Mhd Equations ◽  
Magnetic Diffusion

scholarly journals Global stability solution of the 2D MHD equations with mixed partial dissipation

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Yana Guo ◽  
Yan Jia ◽  
Bo-Qing Dong
Keyword(s):  
Magnetic Field ◽  
Global Stability ◽  
Mhd Equations ◽  
Bootstrap Argument ◽  
Partial Dissipation ◽  
Background Magnetic Field ◽  
Mhd System

<p style='text-indent:20px;'>This paper is devoted to understanding the global stability of perturbations near a background magnetic field of the 2D magnetohydrodynamic (MHD) equations with partial dissipation. We establish the global stability for the solutions of the nonlinear MHD system by the bootstrap argument.</p>

Global well-posedness for the 2D MHD equations without magnetic diffusion in a strip domain

Nonlinearity ◽  
2016 ◽  
Vol 29 (4) ◽  
pp. 1257-1291 ◽  
Author(s):  
Xiaoxia Ren ◽  
Zhaoyin Xiang ◽  
Zhifei Zhang
Keyword(s):  
Mhd Equations ◽  
Well Posedness ◽  
Magnetic Diffusion ◽  
Strip Domain
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