scholarly journals Local Well-Posedness for the Hall-MHD Equations with Fractional Magnetic Diffusion

2015 ◽  
Vol 17 (4) ◽  
pp. 627-638 ◽  
Author(s):  
Dongho Chae ◽  
Renhui Wan ◽  
Jiahong Wu
Keyword(s):  
Mhd Equations ◽  
Well Posedness ◽  
Magnetic Diffusion ◽  
Hall Mhd

scholarly journals Global well-posedness of the full compressible Hall-MHD equations

2021 ◽  
Vol 10 (1) ◽  
pp. 1235-1254
Author(s):  
Qiang Tao ◽  
Canze Zhu
Keyword(s):  
Global Solution ◽  
Large Time ◽  
Initial Temperature ◽  
Large Time Behavior ◽  
Initial Energy ◽  
Mhd Equations ◽  
Well Posedness ◽  
Time Behavior ◽  
Magnetohydrodynamic Flows ◽  
Hall Mhd

Abstract This paper deals with a Cauchy problem of the full compressible Hall-magnetohydrodynamic flows. We establish the existence and uniqueness of global solution, provided that the initial energy is suitably small but the initial temperature allows large oscillations. In addition, the large time behavior of the global solution is obtained.

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

scholarly journals Local Well-Posedness and Blow-Up for the Solutions to the Axisymmetric Inviscid Hall-MHD Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Eunji Jeong ◽  
Junha Kim ◽  
Jihoon Lee
Keyword(s):  
Classical Solution ◽  
Finite Time ◽  
Blow Up ◽  
Mhd Equations ◽  
Well Posedness ◽  
Regular Solutions ◽  
Regularity Problem ◽  
Time Existence ◽  
Hall Mhd

In this paper, we consider the regularity problem of the solutions to the axisymmetric, inviscid, and incompressible Hall-magnetohydrodynamics (Hall-MHD) equations. First, we obtain the local-in-time existence of sufficiently regular solutions to the axisymmetric inviscid Hall-MHD equations without resistivity. Second, we consider the inviscid axisymmetric Hall equations without fluids and prove that there exists a finite time blow-up of a classical solution due to the Hall term. Finally, we obtain some blow-up criteria for the axisymmetric resistive and inviscid Hall-MHD equations.

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