On well-posedness and blow-up for the full compressible Hall-MHD system

2016 ◽  
Vol 31 ◽  
pp. 569-579 ◽  
Author(s):  
Jishan Fan ◽  
Bashir Ahmad ◽  
Tasawar Hayat ◽  
Yong Zhou
Keyword(s):  
Blow Up ◽  
Well Posedness ◽  
Mhd System ◽  
Hall Mhd

On blow-up criteria for a new Hall-MHD system

2016 ◽  
Vol 274 ◽  
pp. 20-24 ◽  
Author(s):  
Jishan Fan ◽  
Bashir Ahmad ◽  
Tasawar Hayat ◽  
Yong Zhou
Keyword(s):  
Blow Up ◽  
Mhd System ◽  
Hall Mhd

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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