ZHANG Rui-feng, GUO Bo-ling. Global Attractor for the Hasegawa-Mima Equation[J]. Applied Mathematics and Mechanics, 2006, 27(5): 505-511.
Citation: ZHANG Rui-feng, GUO Bo-ling. Global Attractor for the Hasegawa-Mima Equation[J]. Applied Mathematics and Mechanics, 2006, 27(5): 505-511.

Global Attractor for the Hasegawa-Mima Equation

  • Received Date: 2004-12-14
  • Rev Recd Date: 2006-01-03
  • Publish Date: 2006-05-15
  • The long time behavior of solution of the Hasegawa-Mima equation with dissipation term is considered. The global attractor problem of the Hasegawa-Mima equation with initial periodic boundary condition was studied. Applying the uniform a priori estimates method, the existence of global attractor of this problem was proved, and also the dimensions of the global attractor are estimated.
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  • [1]
    Hasegawa A,Mima K.Pseudo-three-dimensional turbulence in magnetized nonuniform plasma[J].Phys Fluids,1978,21(1):87—92. doi: 10.1063/1.862083
    Spatschek K H,Zhang W,Naulin V,et al.Self-organization of nonlinear waves and vortices in driven and damped systems[A].In:Debnath L Ed.Nonlinear Dispersive[C].Singapore:World Scientific,1992,507—538.
    Pedlosky J.Geophysical Fluid Dynamics[M].2nd Ed.New York:Springer-Verlag,1987,314—355.
    Bulannov S V,Esirkepov T Zh,Lonfano M,et al.The stability of single and double vortex films in the framework of the Hasegawa-Mima equation[J].Plasma Phys Reports,1997,23(8):660—669.
    Grauer R.An energy estimate for a perturbed Hasegawa-Mima equation[J].Nonlinearity,1998,11(3):659—666. doi: 10.1088/0951-7715/11/3/014
    Kukharkin N,Orszag S A.Generation and structure of Rossby vortices in rotating fluids[J].Phys Rev E,1996,54(5):R4524—R4527.
    Iwayama T,Watanabe T,Shepherd T G.Infrared dynamics of decaying two dimensional turbulence governed by the Charney-Hasegawa-Mima equation[J].J Phys Soc Japan,2001,70(2):376—386. doi: 10.1143/JPSJ.70.376
    GUO Bo-ling,HAN Yong-qian.Existence and uniqueness of global solution of the Hasegawa-Mima equation[J].J Math Phys,2004,45(4):1639—1647. doi: 10.1063/1.1667607
    张瑞凤.广义 Hasegawa-Mima方程整体解的存在惟一性[J].数学的实践与认识,2005,35(8):224—228.
    ZHANG Rui-feng,LI Rui-ge.The global solution for a class of dissipative Hasegawa-Mima equation[J].Chinese Quart J Math,2005,20(4):360—366.
    Temam R.Infinite Dimensional Dynamical Systems in Mechanics and Physics[M].New York:Springer-Verlag,2000,15—329.
    DAI Zheng-de,GUO Bo-ling.Global attractor of nonlinear strain wave-guides[J].Acta Math Sci,Ser B,2000,20(3):322—334.
    Ghidaglia J M.Weakly damped forced Korteweg-de Vries equations behave as a finite dimensional dynamical system in the long time[J].J Differential Equations,1988,74(2):369—390. doi: 10.1016/0022-0396(88)90010-1
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