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
2021 ◽  
Vol 10 (1) ◽  
pp. 1235-1254
Author(s):  
Qiang Tao ◽  
Canze Zhu

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.


Nonlinearity ◽  
2016 ◽  
Vol 29 (4) ◽  
pp. 1257-1291 ◽  
Author(s):  
Xiaoxia Ren ◽  
Zhaoyin Xiang ◽  
Zhifei Zhang

2018 ◽  
Vol 2018 ◽  
pp. 1-16
Author(s):  
Eunji Jeong ◽  
Junha Kim ◽  
Jihoon Lee

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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