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Hasegawa-Mima方程的整体吸引子

张瑞凤 郭柏灵

张瑞凤, 郭柏灵. Hasegawa-Mima方程的整体吸引子[J]. 应用数学和力学, 2006, 27(5): 505-511.
引用本文: 张瑞凤, 郭柏灵. Hasegawa-Mima方程的整体吸引子[J]. 应用数学和力学, 2006, 27(5): 505-511.
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.

Hasegawa-Mima方程的整体吸引子

基金项目: 河南省教育厅自然科学研究基金资助项目(2003110005)
详细信息
    作者简介:

    张瑞凤(1964- ),女,开封市人,教授,博士(联系人.Tel:+86-10-62014411-2547;E-mail:zrf615@henu.edu.cn).

  • 中图分类号: O175.2

Global Attractor for the Hasegawa-Mima Equation

  • 摘要: 考虑了带有耗散项的Hasegawa-Mima方程解的长时间性态, 研究了具有初值周期边值条件的Hasegawa-Mima方程的整体吸引子问题.运用关于时间的一致先验估计,证明了该问题整体吸引子的存在性,并获得了整体吸引子的维数估计.
  • [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
    [2] 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.
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    [5] 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
    [6] Kukharkin N,Orszag S A.Generation and structure of Rossby vortices in rotating fluids[J].Phys Rev E,1996,54(5):R4524—R4527.
    [7] 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
    [8] 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
    [9] 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.
    [10] 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.
    [11] Temam R.Infinite Dimensional Dynamical Systems in Mechanics and Physics[M].New York:Springer-Verlag,2000,15—329.
    [12] DAI Zheng-de,GUO Bo-ling.Global attractor of nonlinear strain wave-guides[J].Acta Math Sci,Ser B,2000,20(3):322—334.
    [13] 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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出版历程
  • 收稿日期:  2004-12-14
  • 修回日期:  2006-01-03
  • 刊出日期:  2006-05-15

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