Pullback attractors for non-autonomous 2D MHD equations on some unbounded domains

2015 ◽  
Vol 113 (2) ◽  
pp. 129-154 ◽  
Author(s):  
Cung The Anh ◽  
Dang Thanh Son
Keyword(s):  
Unbounded Domains ◽  
Mhd Equations ◽  
Pullback Attractors

scholarly journals Backwards Asymptotically Autonomous Dynamics for 2D MHD Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-11
Author(s):  
Jiali Yu ◽  
Wenhuo Su ◽  
Dongmei Xu
Keyword(s):  
Topological Property ◽  
Existence Result ◽  
Mhd Equations ◽  
Pullback Attractors

We consider the backwards topological property of pullback attractors for the nonautonomous MHD equations. Under some backwards assumptions of the nonautonomous force, it is shown that the theoretical existence result for such an attractor is derived from an increasing, bounded pullback absorbing and the backwards pullback flattening property. Meanwhile, some abstract results on the convergence of nonautonomous pullback attractors in asymptotically autonomous problems are established and applied to MHD equations.

Wong–Zakai approximations and attractors for stochastic degenerate parabolic equations on unbounded domains

2020 ◽  
pp. 2150033
Author(s):  
Fahe Miao ◽  
Hui Liu ◽  
Jie Xin
Keyword(s):  
White Noise ◽  
Parabolic Equations ◽  
Existence And Uniqueness ◽  
Stationary Process ◽  
Unbounded Domains ◽  
Degenerate Parabolic Equations ◽  
Pullback Attractors ◽  
Multiplicative White Noise ◽  
Degenerate Parabolic

The Wong–Zakai approximations given by a stationary process and attractors for stochastic degenerate parabolic equations are considered in this paper. We first establish the existence and uniqueness of tempered pullback attractors for the Wong–Zakai approximations of stochastic degenerate parabolic equations. We then prove that the attractors of Wong–Zakai approximations converge to the attractor of stochastic degenerate parabolic equations driven by multiplicative white noise.

Pullback attractors for 2D MHD equations with delays

2021 ◽  
Vol 62 (7) ◽  
pp. 072704
Author(s):  
Xiaoya Song ◽  
Yangmin Xiong
Keyword(s):  
Mhd Equations ◽  
Pullback Attractors

scholarly journals THE ARTIFICIAL COMPRESSIBILITY APPROXIMATION FOR MHD EQUATIONS IN UNBOUNDED DOMAIN

2013 ◽  
Vol 10 (01) ◽  
pp. 181-198 ◽  
Author(s):  
DONATELLA DONATELLI
Keyword(s):  
Wave Equation ◽  
Weak Solution ◽  
Unbounded Domains ◽  
Mhd Equations ◽  
Magnetohydrodynamic Equations ◽  
Artificial Compressibility ◽  
Dispersive Estimate ◽  
Artificial Compressibility Method ◽  
Mhd System ◽  
Incompressible Magnetohydrodynamic Equations

We analyze a method of approximation for the weak solutions of the incompressible magnetohydrodynamic equations (MHD) in unbounded domains. In particular we describe an hyperbolic version of the so-called artificial compressibility method adapted to the MHD system. By exploiting the wave equation structure of the approximating system we achieve the convergence of the approximating sequences by means of dispersive estimate of Strichartz type. We prove that the soleinoidal component of the approximating velocity and magnetic fields is relatively compact and converges strongly to a weak solution of the MHD equation.

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