Global random attractors for the stochastic dissipative Zakharov equations

  • Yan-feng GuoEmail author
  • Bo-ling Guo
  • Dong-long Li


The stochastic dissipative Zakharov equations with white noise are mainly investigated. The global random attractors endowed with usual topology for the stochastic dissipative Zakharov equations are obtained in the sense of usual norm. The method is to transform the stochastic equations into the corresponding partial differential equations with random coefficients by Ornstein-Uhlenbeck process. The crucial compactness of the global random attractors will be obtained by decomposition of solutions.


stochastic dissipative Zakharov equations global random attractors Ornstein-Uhlenbeck process compactness 

2000 MR Subject Classification

35Q35 60H15 


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  1. [1]
    Bejenaru, I., Herr, S., Holmer, J., Tataru, D. On the 2d Zakharov equations with L 2 Schrö dinger data. Nonlinearity, 22: 1063–1089 (2009)CrossRefzbMATHMathSciNetGoogle Scholar
  2. [2]
    Crauel, H., Flandoli, F. Attractors for random dynamical systems. Probab. Theory Rel., 100: 365–393 (1994)CrossRefzbMATHMathSciNetGoogle Scholar
  3. [3]
    Crauel, H., Debussche, A., Flandoli, F. Random attractors. J. Dyn. Differ. Equ., 9: 307–341 (1997)CrossRefzbMATHMathSciNetGoogle Scholar
  4. [4]
    E, W., Li, X., Vanden-Eijnden, E. Some recent progress in multiscale modeling, Multiscale modeling and simulation. Lect. Notes in Computer Science Engineering, Springer-Verlag, Berlin, 39: 3–21 (2004)Google Scholar
  5. [5]
    Flahaut, I. Attractors for the dissipative Zakharov equations. Nonlinear Anal. TMA., 16(7): 599–633 (1991)CrossRefzbMATHMathSciNetGoogle Scholar
  6. [6]
    Goubet, O., Moise, I. Attractors for dissipative Zakharov equations. Nonlinear Anal. TMA., 31(7): 823–847 (1998)CrossRefzbMATHMathSciNetGoogle Scholar
  7. [7]
    Guio, P., Forme, F. Zakharov simulations of Langmuir turbulence: Effects on the ion-acoustic waves in incoherent scattering. Phys. Plasmas, 13: 122902–10 (2006)CrossRefGoogle Scholar
  8. [8]
    Guo, B. On the IBVP for some more extensive Zakharov equations. J. Math., 7(3): 269–275 (1987)Google Scholar
  9. [9]
    Guo, B., Lv, Y., Yang, X. Dynamics of Stochastic Zakharov Equations. J. Math. Phys., 50: 052703 (2009)Google Scholar
  10. [10]
    Guo, Y., Dai, Z., Li, D. Explicit Heteroclinic Tube Solutions for the Zakharov System with Periodic Boundary. Chin. J. Phys., 46(5): 570–577 (2008)Google Scholar
  11. [11]
    Imkeller, P., Monahan, A.H. Conceptual stochastic climate models. Stoch. Dynam., 2: 311–326 (2002)CrossRefzbMATHMathSciNetGoogle Scholar
  12. [12]
    Li, Y. On the initial boundary value problems for two dimensional systems of Zakharov equations and of complex-Schrödinger-real-Boussinesq equations. J. Partial Differential Equations., 5(2): 81–93 (1992)MathSciNetGoogle Scholar
  13. [13]
    Masselin, V. A result on the blow-up rate for the Zakharov equations in dimension 3. SIAM J. Math. Anal., 33(2): 440–447 (2001)CrossRefzbMATHMathSciNetGoogle Scholar
  14. [14]
    Temam, R. Infinite-dimensional Dynamical Systems in Mechanics and Physics. Springer-Verlag, New York, 1988CrossRefzbMATHGoogle Scholar
  15. [15]
    Wang, B. Random attractors for the stochastic Benjamin-Bona-Mahony equation on unbounded domains. J. Diff. Equ., 246: 2506–2537 (2009)CrossRefzbMATHGoogle Scholar
  16. [16]
    Wang, B. Random attractors for the stochastic FitzHugh-Nagumo equations on unbounded domains. Nonlinear Anal. TMA., 71(7-8): 2811–2828 (2009)CrossRefzbMATHGoogle Scholar
  17. [17]
    Zakharov, V.E. Collapse of Langmuir waves. Sov. Phys. JETP, 35: 908–914 (1972)Google Scholar

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© Institute of Applied Mathematics, Academy of Mathematics and System Sciences, Chinese Academy of Sciences and Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.College of ScienceGuangxi University of Science and TechnologyLiuzhouChina
  2. 2.Institute of Applied Physics and Computational MathematicsBeijingChina

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