Skip to main content
Log in

Random attractors of boussinesq equations with multiplicative noise

  • Published:
Acta Mathematica Sinica, English Series Aims and scope Submit manuscript

Abstract

We study the random dynamical system (RDS) generated by the Benald flow problem with multiplicative noise and prove the existence of a compact random attractor for such RDS.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

We’re sorry, something doesn't seem to be working properly.

Please try refreshing the page. If that doesn't work, please contact support so we can address the problem.

References

  1. Temam, R.: Infinite-dimensional dynamical systems in Mechanics and Physics, Springer-Verlag, New York, 1988

    MATH  Google Scholar 

  2. Guo, B. L.: Nonlinear Galerkin methods for solving two dimensional Boussinesq equations. Chin. Ann. of Math., 16B, 379–390 (1995)

    Google Scholar 

  3. Guo, B. L.: Spectral methods for solving two dimension Newton-Boussinesq equations. Acta Math. Appl. Sinica, 5, 208–218 (1989)

    Article  MATH  Google Scholar 

  4. Guo, B. L., Wang, B. X.: Exponential attractors for the generalized Ginzburg-Landau equation. Acta Mathematica Sinica, Chinese Series, 16(3), 515–526 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  5. Lu, S. J., Lu, Q. S.: Exponential attractors of the 3D derivative Ginzburg-Landau equation. Acta Mathematica Sinica, English Series, 24(5), 809–828 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  6. Shen, C. X., Guo, B. L.: Ill-posedness for the nonlinear Davey-Stewartson equation. Acta Mathematica Sinica, English Series, 24(1), 117–127 (2008)

    Article  MathSciNet  Google Scholar 

  7. Zhang, W. N.: Dimension of Maximal attractors for the m-dimensional Cahn-Hilliard system. Acta Mathematica Sinica, English Series, 21(6), 1487–1494 (2005)

    Article  MATH  MathSciNet  Google Scholar 

  8. Amold, L.: “Random dynamical system”, Springer Monographs in Mathematics, Springer-Verlag, Berlin, 1998

    Google Scholar 

  9. Caraballo, T., Langa, J. A.: Stability and random attractors for a reaction-diffusion equation with multiplicative noise. Discrete Contin. Dyn. Syst. 6, 875–892 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  10. Caraballo, T., Langa, J. A., Robinson, J. C.: Upper semicontinuity of attractors for random perturbations of dynamical systems. Commun. Partial Diff. Equ., 23, 1557–1581 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  11. Crauel, H., Debussche, A., Flandoli, F.: Random attractors. J. Dyn Diff. Equ., 9, 307–341 (1995)

    Article  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  13. Debussche, A.: Hausdorff dimension of a random invariant set. J. Math. Pures Appl., 77, 967–988 (1998)

    MATH  MathSciNet  Google Scholar 

  14. Fan, X. M.: Random attractor for a damped sine-Gordon equation with white noise. Pacific J. Math., 216, 63–76 (2004)

    Article  MATH  MathSciNet  Google Scholar 

  15. Prato, G., Da Debussche, A., Temam, R.: Stochastic Burger’s equations. Nonlin. Diff. Eq. Appl., 1, 389–402 (1994)

    Article  MATH  Google Scholar 

  16. Robinson, J. C.: Stability of random attractors under perturbation and approximation. J. Diff. Equ., 186, 652–669 (2002)

    Article  MATH  Google Scholar 

  17. Wang, G. L., Guo, B. L., Li, Y. R.: The asymptotic behavior of the stochastic Ginzburg-Landau equation with additive noise. Appl. Math. Computation, 198, 849–857 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  18. Yang, D. S.: The asymptotic behavior of the stochastic Ginzburg-Landau equation with multiplicative noise. J. Math. Physics, 45, 4064–4076 (2004)

    Article  MATH  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Yang Rong Li.

Additional information

Supported by the China Postdoctoral Science Foundation (No. 2005038326)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Li, Y.R., Guo, B.L. Random attractors of boussinesq equations with multiplicative noise. Acta. Math. Sin.-English Ser. 25, 481–490 (2009). https://doi.org/10.1007/s10114-008-6226-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10114-008-6226-0

Keywords

MR(2000) Subject Classification

Navigation