Skip to main content
Log in

H 2-regularity random attractors of stochastic non-Newtonian fluids with multiplicative noise

  • Published:
Applied Mathematics and Mechanics Aims and scope Submit manuscript

Abstract

In this paper, the authors study the long time behavior of solutions to stochastic non-Newtonian fluids in a two-dimensional bounded domain, and prove the existence of H 2-regularity random attractor.

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.

Institutional subscriptions

Similar content being viewed by others

References

  1. Bellout, H., Bloom, F., and Nečas, J. Young measure-valued solutions for non-Newtonian incompressible viscous fluids. Communications in Partial Differential Equations, 19, 1763–1803 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  2. Bloom, F. Attractors of non-newtonian fluids. J. Dyn. Differ. Equ., 7(1), 109–140 (1995)

    Article  MATH  Google Scholar 

  3. Bloom, F. and Hao, W. Regularization of a non-Newtonian system in an unbounded channel: existence of a maximal compact attractor. Nonlinear Analysis: Theory, Methods & Applications, 43, 743–766 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  4. Guo, B., Lin, G., and Shang, Y. Non-Newtonian Fluids Dynamical Systems (in Chinese), National Defense Industry Press, Beijing (2006)

    Google Scholar 

  5. Zhao, C. and Zhou, S. Pullback attractors for a non-autonomous incompressible non-Newtonian fluid. J. Diff. Equ., 238, 394–425 (2007)

    Article  MATH  MathSciNet  Google Scholar 

  6. Zhao, C. and Li, Y. A note on the asymptotic smoothing effect of solutions to a non-Newtonian system in 2-D unbounded domains. Nonlinear Analysis, 60, 475–483 (2005)

    MATH  MathSciNet  Google Scholar 

  7. Guo, B. and Guo, C. The convergence of non-Newtonian fuids to Navier-Stokes equations. J. Math. Anal. Appl., 357, 468–478 (2009)

    Article  MATH  MathSciNet  Google Scholar 

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

    Article  MATH  MathSciNet  Google Scholar 

  9. Crauel, H. and Flandoli, F. Attractors for random dynamical systems. Probality Theory and Related Fields, 100, 365–393 (1994)

    Article  MATH  MathSciNet  Google Scholar 

  10. Da Prato, G., Debussche, A., and Temam, R. Stochastic Burgers’ equation. Nonlinear Differential Equations and Applications, 1, 389–402 (1994)

    Article  MATH  Google Scholar 

  11. De Bouard, A. and Debussche, A. On the stochastic Korteweg-de Vries equation. Journal of Functional Analysis, 154, 215–251 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  12. De Bouard, A. and Debussche, A. A stochastic nonlinear Schrödinger equation with multiplicative noise. Commun. Math. Phys., 205, 161–181 (1999)

    Article  MATH  Google Scholar 

  13. Krylov, N. V. and Rozovsikii, B. L. Stochastic evolution equations (in Russian). Journal of Soviet Mathematics, 16, 1233–1277 (1981)

    Article  MATH  Google Scholar 

  14. Da Prato, G. and Zabczyk, J. Stochastic Equations in Infinite Dimensions, Cambridge University Press, Cambridge (1992)

    Book  MATH  Google Scholar 

  15. Guo, B., Guo, C., and Han, Y. Random attractors of stochastic non-Newtonian fluid. Acta Math. Appl. Sin., 28, 165–180 (2012)

    Article  MathSciNet  Google Scholar 

  16. Guo, B., Guo, C., and Zhang, J. Martingale and stationary solutions for stochastic non-Newtonian fluids. Diff. Int. Equ., 23, 303–326 (2010)

    MATH  Google Scholar 

  17. Zhao, C. and Duan, J. Random attractor for the Ladyzhenskaya model with additive noise. J. Math. Anal. Appl., 362, 241–251 (2010)

    Article  MATH  MathSciNet  Google Scholar 

  18. Li, J. and Huang, J. H. Dynamics of 2D Stochastic non-Newtonian fluids driven by fractional Brownian motion, Appl. Math. Mech. -Engl. Ed., 34(2), 189–208 (2013) DOI 10.1007/s10483-013-1663-6

    Article  MATH  Google Scholar 

  19. Zhao, C., Li, Y., and Zhou, S. Random attractor for a two-dimensional incompressible non-Newtonian fluid with multiplicative noise. Acta Mathematica Scientia, 31, 567–575 (2011)

    Article  MATH  MathSciNet  Google Scholar 

  20. Guo, C. and Guo, B. Remark on random attractor for a two dimensional incompressible non-Newtonian fluid with multiplicative noise. Commun. Math. Sci., 10, 821–833 (2012)

    Article  MATH  MathSciNet  Google Scholar 

  21. Zhao, C. and Li, Y. H 2-compact attractor for a non-Newtonian system in two-dimensional unbounded domains. Nonlinear Analysis, 56, 1091–1103 (2004)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Chun-xiao Guo  (郭春晓).

Additional information

Project supported by the National Natural Science Foundation of China (Nos. 11126160, 11201475, 11371183, and 11101356)

Rights and permissions

Reprints and permissions

About this article

Cite this article

Guo, Cx., Guo, Bl. & Yang, H. H 2-regularity random attractors of stochastic non-Newtonian fluids with multiplicative noise. Appl. Math. Mech.-Engl. Ed. 35, 105–116 (2014). https://doi.org/10.1007/s10483-014-1776-7

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10483-014-1776-7

Key words

Chinese Library Classification

2010 Mathematics Subject Classification

Navigation