scholarly journals Global weak solutions and long time behavior for 1D compressible MHD equations without resistivity

2019 ◽  
Vol 60 (7) ◽  
pp. 071511 ◽  
Author(s):  
Yang Li ◽  
Yongzhong Sun
Keyword(s):  
Weak Solutions ◽  
Mhd Equations ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Global Weak Solutions ◽  
Long Time ◽  
Compressible Mhd Equations

scholarly journals On the Dynamics of Controlled Magnetohydrodynamic Systems

2008 ◽  
Vol 13 (3) ◽  
pp. 351-377 ◽  
Author(s):  
S. S. Ravindran
Keyword(s):  
Optimal Control ◽  
Optimal Control Problem ◽  
Control Problem ◽  
Optimal Solution ◽  
Mhd Equations ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Existence Of A Solution ◽  
Decay Properties ◽  
Long Time

In this paper we study the long time behavior of solutions for an optimal control problem associated with the viscous incompressible electrically conducting fluid modeled by the magnetohydrodynamic (MHD) equations in a bounded two dimensional domain through the adjustment of distributed controls. We first construct a quasi-optimal solution for the MHD systems which possesses exponential decay in time. We then derive some preliminary estimates for the long-time behavior of all admissible solutions of the MHD systems. Next we prove the existence of a solution for the optimal control problem for both finite and infinite time intervals. Finally, we establish the long-time decay properties of the solutions for the optimal control problem.

scholarly journals LONG TIME BEHAVIOR OF STOCHASTIC MHD EQUATIONS PERTURBED BY MULTIPLICATIVE NOISES

2016 ◽  
Vol 6 (4) ◽  
pp. 1081-1104 ◽  
Author(s):  
Hongyong Cui ◽  
◽  
Yangrong Li ◽  
Jinyan Yin
Keyword(s):  
Mhd Equations ◽  
Time Behavior ◽  
Long Time Behavior ◽  
Multiplicative Noises ◽  
Long Time

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]}.

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