Asymptotic behavior of two-dimensional stochastic magneto-hydrodynamics equations with additive noises

This paper is devoted to the investigation of the asymptotic behavior of solutions of the stochastic magneto-hydrodynamics equations driven by random exterior forced terms both in the velocity and in the magnetic field. The nonlinear term is supposed to be time-dependent and satisfies certain dissipative conditions. The existence of a random attractor for this random dynamical system is obtained.

[1]  L. Arnold.  Random Dynamical Systems , 2003 .

[2]  Endre Süli,et al.  Large-time behaviour of solutions to the magneto-hydrodynamics equations , 1996 .

[3]  R. Temam.  Infinite Dimensional Dynamical Systems in Mechanics and Physics Springer Verlag , 1993 .

[4]  Peter E. Kloeden,et al.  Flattening, squeezing and the existence of random attractors , 2007, Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[5]  Tomás Caraballo,et al.  Stability and random attractors for a reaction-diffusion equation with multiplicative noise , 2000 .

[6]  Zdzislaw Brzezniak,et al.  Asymptotic compactness and absorbing sets for 2D stochastic Navier-Stokes equations on some unbounded domains , 2006 .

[7]  Dongjuan Niu,et al.  MATHEMATICAL RESULTS RELATED TO A TWO-DIMENSIONAL MAGNETO-HYDRODYNAMIC EQUATIONS * * The research is , 2006 .

[8]  Boling Guo,et al.  Random attractors for quasi-continuous random dynamical systems and applications to stochastic reaction–diffusion equations☆ , 2008 .

[9]  V. Barbu,et al.  Existence and Ergodicity for the Two-Dimensional Stochastic Magneto-Hydrodynamics Equations , 2007 .

[10]  M. Weinstein.  Nonlinear Schrödinger equations and sharp interpolation estimates , 1983 .

[11]  Bin Wang,et al.  Random attractors of reaction-diffusion equations with multiplicative noise in Lp , 2010, Appl. Math. Comput..

[12]  Yangrong Li,et al.  The asymptotic behavior of the stochastic Ginzburg-Landau equation with additive noise , 2008, Appl. Math. Comput..

[13]  R. Sasaki,et al.  Solution of the dual reflection equation for An−1(1) solid-on-solid model , 2003, hep-th/0308118.

[14]  Jinqiao Duan,et al.  Random attractor for the Ladyzhenskaya model with additive noise , 2010 .

[15]  Roger Temam,et al.  Some mathematical questions related to the MHD equations , 1983 .

[16]  H. Crauel,et al.  Attractors for random dynamical systems , 1994 .

[17]  T. Ozawa,et al.  Global Cauchy Problem for the 2-D Magnetohydrodynamic-α Models with Partial Viscous Terms , 2010 .

[18]  Lin Zhao,et al.  Uniqueness of ground states of some coupled nonlinear Schrodinger systems and their application , 2007, 0708.0284.

[19]  Song Jiang,et al.  Incompressible Limit of the Compressible Magnetohydrodynamic Equations with Periodic Boundary Conditions , 2009, 1010.5296.

[20]  B. Guo,et al.  Random attractors of boussinesq equations with multiplicative noise , 2009 .

[21]  F. Flandoli,et al.  Random attractors for the 3D stochastic Navier-Stokes equation with multiplicative white noise , 1996 .