GAO Hong-jun, DUAN Jin-qiao. Averaging Principle for Quasi-Geostrophic Motion Under Rapidly Oscillating Forcing[J]. Applied Mathematics and Mechanics, 2005, 26(1): 99-110.
Citation: GAO Hong-jun, DUAN Jin-qiao. Averaging Principle for Quasi-Geostrophic Motion Under Rapidly Oscillating Forcing[J]. Applied Mathematics and Mechanics, 2005, 26(1): 99-110.

Averaging Principle for Quasi-Geostrophic Motion Under Rapidly Oscillating Forcing

  • Received Date: 2003-04-01
  • Rev Recd Date: 2004-09-14
  • Publish Date: 2005-01-15
  • A class of large scale geophysical fluid fows are modelled by the quasi-geostrophic equation.An averaging principle for quasi-geostrophic motion under rapidly oscil-lating(non-autonomous) forcing was obtained,both on finite but large time intervals and on the entire time axis.This includes comparison estimate,stability estimate,and convergence result between quasi-geostrophic motions and its averaged motions.Furthermore,the existence of almost periodic quasi-geostrophic motions and attractor convergence were also investigated.
  • loading
  • [1]
    Pedlosky J.Geophysical Fluid Dynamics[M].2nd ed.Berlin,New York:Springer-Verlag,1987.
    Pedlosky J.Ocean Circulation Theory[M].Berlin:Springer-Verlag,1996.
    Cessi P,Ierley G R.Symmetry-breaking multiple equilibria in quasigeostrophic, wind-driven flows[J].J Phys Oceanography,1995,25(3):1196—1205. doi: 10.1175/1520-0485(1995)025<1196:SBMEIQ>2.0.CO;2
    Milliff R F,Morzel J.The global distribution of the time-average wind stress curl from nscat[J].J Atmos Sci,2001,58(5):109—131. doi: 10.1175/1520-0469(2001)058<0109:TGDOTT>2.0.CO;2
    Gilbarg D,Trudinger N S.Elliptic Partial Differential Equations of Second Order[M].2nd ed.Berlin, New York:Springer-Verlag,1983.
    Henry D.Geometric Theory of Semilinear Parabolic Equations[M].New York:Springer-Verlag,1981.
    Duan J,Kloeden P E.Dissipative quasigeostrophic motion under temporally almost periodic forcing[J].J Math Anal Appl,1999,236(1):74—85. doi: 10.1006/jmaa.1999.6432
    Levitan B M,Zhilov V V.Almost Periodic Functions and Differential Equations[M].Cambridge:Cambridge University Press,1982.(English version)
    Ilyin A A.Averaging principle for dissipative dynamical system with rapidly oscillating right-hand sides[J].Math Sb,1996,187(5):635—677. doi: 10.1070/SM1996v187n05ABEH000126
    Barcilon V,Constantin P,Titi E S.Existence of solutions to the Stommel-Charney model of the Gulf stream[J].SIAM J Math Anal,1988,19(6):1355—1364. doi: 10.1137/0519099
    Dymnikov V P,Filatov A N.Mathematics of Climate Modeling[M].Boston,Cambridge,MA:Birkhauser,1997.
    Wu J.Inviscid limits and regularity estimates for the solutions of the 2D dissipative quasigeostrophic equations[J].Indiana Univ Math J,1997,46(4):1113—1124.
    Bennett A F,Kloeden P E.The dissipative quasigeostrophic equation[J].Mathematika,1981,28:265—288. doi: 10.1112/S0025579300010329
    Brannan J,Duan J,Wanner T.Dissipative quasigeostrophic dynamics under random forcing[J].J Math Anal Appl,1998,228(1):221—233. doi: 10.1006/jmaa.1998.6128
    Duan J.Time periodic quasigeostrophic motion under dissipation and forcing[J].Appl Math Comput,1999,102(2/3):121—127. doi: 10.1016/S0096-3003(98)10034-6
    Babin A V,Vishik M I.Attractor of Evolution Equations[M].Amsterdam:North-Holland,1992.(English version)
    Hale J K.Asymptotic Behavior for Dissipative Dynamical System[M].Providence,RI:Amer Math Soc, 1988.
    Temam R.Infinite-Dimensional Dynamical Systems in Mechanics and Physics[M].New York:Springer-Verlag,1988.
    Kato T.Perturbation Theory for Linear Operators[M].New York:Springer-Verlag,1966.
    Chepyzhov V V,Vishik M I.Non-Autonomous Dynamical Systems and Their Attractors, Appendix in the book: M I Vishik.Asymptotic Behavior of Solutions of Evolutionary Equations[M].Cambridge:Cambridge Univ Press,1992.
    Chepyzhov V V,Vishik M I.A Hausdorff dimension estimate for kernal sections of non-autonomous evolution equations[J].Indiana Univ Math J,1993,42(3):1057—1076. doi: 10.1512/iumj.1993.42.42049
    Chepyzhov V V,Vishik M I.Attractors of non-autonomous dynamical systems and their dimension[J].J Math Pures Appl,1994,73(3):279—333.
  • 加载中


    通讯作者: 陈斌,
    • 1. 

      沈阳化工大学材料科学与工程学院 沈阳 110142

    1. 本站搜索
    2. 百度学术搜索
    3. 万方数据库搜索
    4. CNKI搜索

    Article Metrics

    Article views (2320) PDF downloads(601) Cited by()
    Proportional views


    DownLoad:  Full-Size Img  PowerPoint