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Global random attractors for the stochastic dissipative Zakharov equations

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Abstract

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.

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References

  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)

    Article  MATH  MathSciNet  Google Scholar 

  2. Crauel, H., Flandoli, F. Attractors for random dynamical systems. Probab. Theory Rel., 100: 365–393 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  3. Crauel, H., Debussche, A., Flandoli, F. Random attractors. J. Dyn. Differ. Equ., 9: 307–341 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  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. Flahaut, I. Attractors for the dissipative Zakharov equations. Nonlinear Anal. TMA., 16(7): 599–633 (1991)

    Article  MATH  MathSciNet  Google Scholar 

  6. Goubet, O., Moise, I. Attractors for dissipative Zakharov equations. Nonlinear Anal. TMA., 31(7): 823–847 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    Article  Google Scholar 

  8. Guo, B. On the IBVP for some more extensive Zakharov equations. J. Math., 7(3): 269–275 (1987)

    Google Scholar 

  9. Guo, B., Lv, Y., Yang, X. Dynamics of Stochastic Zakharov Equations. J. Math. Phys., 50: 052703 (2009)

    Google Scholar 

  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. Imkeller, P., Monahan, A.H. Conceptual stochastic climate models. Stoch. Dynam., 2: 311–326 (2002)

    Article  MATH  MathSciNet  Google Scholar 

  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)

    MathSciNet  Google Scholar 

  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)

    Article  MATH  MathSciNet  Google Scholar 

  14. Temam, R. Infinite-dimensional Dynamical Systems in Mechanics and Physics. Springer-Verlag, New York, 1988

    Book  MATH  Google Scholar 

  15. Wang, B. Random attractors for the stochastic Benjamin-Bona-Mahony equation on unbounded domains. J. Diff. Equ., 246: 2506–2537 (2009)

    Article  MATH  Google Scholar 

  16. Wang, B. Random attractors for the stochastic FitzHugh-Nagumo equations on unbounded domains. Nonlinear Anal. TMA., 71(7-8): 2811–2828 (2009)

    Article  MATH  Google Scholar 

  17. Zakharov, V.E. Collapse of Langmuir waves. Sov. Phys. JETP, 35: 908–914 (1972)

    Google Scholar 

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Authors and Affiliations

  1. College of Science, Guangxi University of Science and Technology, Liuzhou, 545006, China

    Yan-feng Guo & Dong-long Li

  2. Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088, China

    Yan-feng Guo & Bo-ling Guo

Authors
  1. Yan-feng Guo
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  2. Bo-ling Guo
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  3. Dong-long Li
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Correspondence to Yan-feng Guo.

Additional information

Supported by the National Natural Science Foundation of China (No. 11061003,11301097), Guangxi Natural Science Foundation Grant (No. 2013GXNSFAA019001) and Guangxi Science Research Item (No. 2013YB170).

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Guo, Yf., Guo, Bl. & Li, Dl. Global random attractors for the stochastic dissipative Zakharov equations. Acta Math. Appl. Sin. Engl. Ser. 30, 289–304 (2014). https://doi.org/10.1007/s10255-014-0288-9

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  • DOI: https://doi.org/10.1007/s10255-014-0288-9

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