scholarly journals Global solution to the 3-D inhomogeneous incompressible MHD system with discontinuous density

2019 ◽  
Vol 12 (1) ◽  
pp. 37-58 ◽  
Author(s):  
Fei Chen ◽  
◽  
Boling Guo ◽  
Xiaoping Zhai ◽  
◽  
...  
Keyword(s):  
Global Solution ◽  
Mhd System ◽  
Incompressible Mhd

Long time behavior of solutions to 3D generalized MHD equations

2020 ◽  
Vol 32 (4) ◽  
pp. 977-993
Author(s):  
Xiaopeng Zhao
Keyword(s):  
Fractional Laplacian ◽  
Mhd Equations ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Algebraic Decay ◽  
Generalized Mhd Equations ◽  
Long Time ◽  
Whole Space ◽  
Mhd System ◽  
Incompressible Mhd

AbstractIn this paper, we consider the long time behavior of solutions for 3D incompressible MHD equations with fractional Laplacian. Firstly, in a periodic bounded domain, we prove the existence of a global attractor. The analysis reveals a relation between the Laplacian exponent and the regularity of the spaces of velocity and magnetic fields. Finally, in the whole space {\mathbb{R}^{3}}, we establish the sharp algebraic decay rate of solutions to the generalized MHD system provided that the parameters satisfy {\alpha,\beta\in(0,2]}.

scholarly journals Global small solutions of 2-D incompressible MHD system

2015 ◽  
Vol 259 (10) ◽  
pp. 5440-5485 ◽  
Author(s):  
Fanghua Lin ◽  
Li Xu ◽  
Ping Zhang
Keyword(s):  
Mhd System ◽  
Incompressible Mhd
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