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含线性阻尼的2D非自治gNavier--Stokes方程的拉回吸引子

姜金平 侯延仁 王小霞

姜金平, 侯延仁, 王小霞. 含线性阻尼的2D非自治gNavier--Stokes方程的拉回吸引子[J]. 应用数学和力学, 2011, 32(2): 144-157. doi: 10.3879/j.issn.1000-0887.2011.02.003
引用本文: 姜金平, 侯延仁, 王小霞. 含线性阻尼的2D非自治gNavier--Stokes方程的拉回吸引子[J]. 应用数学和力学, 2011, 32(2): 144-157. doi: 10.3879/j.issn.1000-0887.2011.02.003
JIANG Jin-ping, HOU Yan-ren, WANG Xiao-xia. Pullback Attractor of 2D Nonautonomous g-Navier-Stokes Equations With Linear Dampness[J]. Applied Mathematics and Mechanics, 2011, 32(2): 144-157. doi: 10.3879/j.issn.1000-0887.2011.02.003
Citation: JIANG Jin-ping, HOU Yan-ren, WANG Xiao-xia. Pullback Attractor of 2D Nonautonomous g-Navier-Stokes Equations With Linear Dampness[J]. Applied Mathematics and Mechanics, 2011, 32(2): 144-157. doi: 10.3879/j.issn.1000-0887.2011.02.003

含线性阻尼的2D非自治gNavier--Stokes方程的拉回吸引子

doi: 10.3879/j.issn.1000-0887.2011.02.003
基金项目: 国家自然科学基金资助项目(10871156);西安交通大学专项基金(2009xjtujc30)的资助
详细信息
    作者简介:

    姜金平(1974- ),男,陕西洛川人,副教授,博士(E-mail:yadxjjp@163.com);侯延仁(1969- ),男,陕西延安人,教授,博士生导师(联系人.E-mail:yrhou@mail.xjtu.edu.cn).

  • 中图分类号: O175;O35

Pullback Attractor of 2D Nonautonomous g-Navier-Stokes Equations With Linear Dampness

  • 摘要: 讨论了无界区域上含线性阻尼的2D非自治 g-Navier-Stokes 方程的拉回吸引子,通过验证共圈的拉回D-吸收集的存在性和拉回D-渐近紧性,证明了含线性阻尼的2D非自治 g-Navier-Stokes 方程的拉回吸引子的存在性,并给出了拉回吸引子的Fractal维数估计.
  • [1] Roh J. g-Navier-Stokes equations[D]. Ph D Dissertation. Minnesota: University of Minnesota, 2001.
    [2] Roh J. Dynamics of the g-Navier-Stokes equations[J]. J Differential Equations, 2005, 211(2):452-484. doi: 10.1016/j.jde.2004.08.016
    [3] JIANG Jin-ping, HOU Yan-ren. The global attractor of g-Navier-Stokes equations with linear dampness on R2[J].Appl Math Comput, 2009, 215(3):1068-1076. doi: 10.1016/j.amc.2009.06.035
    [4] 姜金平, 侯延仁. 有界区域上2D非自治g-Navier-Stokes方程的拉回吸引子[J].应用数学和力学, 2010, 31(6): 670-680.(JIANG Jin-ping, HOU Yan-ren. Pullback attractor of 2D non-autonomous g-Navier-Stokes equations on some bounded domains[J].Applied Mathematics and Mechanics(English Edition), 2010, 31(6):697-708.)
    [5] Kwak M, Kwean H, Roh J. The dimension of attractor of the 2D g-Navier-Stokes equations[J]. J Math Anal Appl, 2006, 315(2):436-461. doi: 10.1016/j.jmaa.2005.04.050
    [6] Babin A V, Vishik M I. Attractors of partial differential equations in an unbounded domain[J]. Proc Roy Soc Edinburgh Sect A, 1990, 116:221-243. doi: 10.1017/S0308210500031498
    [7] Constantin P, Foia C, Temam R. Attractor Representing Turbulent Flows[M]. Mem Amer Math Soc, 1985, 53(314):1-67.
    [8] Rosa R. The global attractor for the 2D-Navier-Stokes flow in some unbounded domain[J]. Nonlinear Analysis, Theory, Methods and Applications, 1998, 32(1):71-85. doi: 10.1016/S0362-546X(97)00453-7
    [9] Cheban D N, Duan J. Almost periodic solutions and global attractors of nonautonomous Navier-Stokes equation[J]. J Dyn Differ Equation, 2004, 16(1):1-34. doi: 10.1023/B:JODY.0000041279.25095.8a
    [10] Cheban D N. Global Attractors of Non-Autonomous Dissipative Dynamical Systems[M]. Singapore:World Scientific, 2004.
    [11] Zhong C K, Yang M H, Sun C Y. The existence of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reaction-diffusion equations[J]. J Diff Eqns, 2006, 223(2):367-399. doi: 10.1016/j.jde.2005.06.008
    [12] Raugel G, Sell G R. Navier-Stokes equations on thin 3D domains—Ⅰ: global attractors and global regularity of solutions[J].J Amer Math Soc, 1993, 6(3):503-568.
    [13] Hou Y R, Li K T. The uniform attractor for the 2D non-autonomous Navier-Stokes flow in some unbounded domain[J].Nonlinear Analysis, 2004, 58(5/6):609-630. doi: 10.1016/j.na.2004.02.031
    [14] Caraballo T, Kloeden P E, Real J. Pullback and forward attractors for a damped wave equation with delays[J]. Stochastics and Dynamics, 2004, 4(3):405-423. doi: 10.1142/S0219493704001139
    [15] Caraballo T, Real J. Attractors for 2D Navier-Stokes models with delays[J].J Differ Equation, 2004, 205(2):271-297. doi: 10.1016/j.jde.2004.04.012
    [16] Caraballo T, Kloden P E, Marin-Rubio P. Global and pullback attractor of set-valued skew product flows[J].Ann Mat, 2006, 185(20):S23-S45.
    [17] Caraballo T, Lukaszewicz G, Real J. Pullback attractors for asymptotically compact nonautonomous dynamical systems[J]. Nonlinear Anal, 2006, 64(3):484-498. doi: 10.1016/j.na.2005.03.111
    [18] Caraballo T, Real J, Chueshov I D. Pullback attractors for stochastic heat equations in materials with memory[J]. Discrote Contin Dyn Syst Ser B, 2008, 9(3):525-539. doi: 10.3934/dcdsb.2008.9.525
    [19] Kloeden P E. Pullback attractors in nonautonomous difference equations[J]. J Differ Equations Appl, 2006, 6(1): 33-52.
    [20] Kloeden P E. Pullback attractors of nonautonomous semidynamical systems[J]. Stoch Dyn, 2003, 3(1):101-112. doi: 10.1142/S0219493703000632
    [21] Song H T, Wu H Q. Pullback attractor of nonautonomous reaction-diffusion equations[J]. J Math Anal Appl, 2007, 325(2):1200-1215. doi: 10.1016/j.jmaa.2006.02.041
    [22] Temam R. Infinite-Dimensional Dynamical System in Mechanics and Physics[M]. Vol 68.Appl Math Sci. New York: Springer-Verlag,1988.
    [23] Langa J A, Lukaszewicz G, Real J. Finite fractal dimension of pullback attractor for non-autonomous 2D Navier-Stokes equations in some unbounded domains[J]. Nonlinear Anal, 2007, 66(3):735-749. doi: 10.1016/j.na.2005.12.017
    [24] Sell G R, You Y. Dynamics of Evolutionary Equations[M]. Applied Mathematical Sciences.Vol 143. New York:Springer, 2002.
    [25] Bae H, Roh J. Existence of solutions of the g-Navier-Stokes equations[J].Taiwanese J Math, 2004, 8(1):85-102.
    [26] Temam R. Navier-Stokes Equations:Theory and Numerical Analysis[M].Providence: AMS Chelsea Publishing, 2001.
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出版历程
  • 收稿日期:  2010-06-05
  • 修回日期:  2011-01-05
  • 刊出日期:  2011-02-15

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