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Acta Mathematicae Applicatae Sinica, English Series 2012, Vol. 28 Issue (1) :165-180    DOI: 10.1007/s10255-012-0132-z
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Random Attractors of Stochastic Non-Newtonian Fluids
Chun-xiao GUO1, Bo-ling GUO2, Yong-qian HAN2
1. Department of Mathematics, China University of Mining and Technology Beijing, Beijing 100083, China;
2. Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
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Abstract The present paper investigates the asymptotic behavior of solutions for stochastic non-Newtonian fluids in a two-dimensional domain. Firstly, we prove the existence of random attractors ΛH(ω) in H; Secondly, we prove the existence of random attractors ΛV (ω) in V. Then we verify regularity of the random attractors by showing that ΛH(ω) = ΛV (ω), which implies the smoothing effect of the fluids in the sense that solution becomes eventually more regular than the initial data.  
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Keywordsrandom attractors   non-Newtonian fluids   additive noise   Ornstein-Uhlenbeck process     
Abstract: The present paper investigates the asymptotic behavior of solutions for stochastic non-Newtonian fluids in a two-dimensional domain. Firstly, we prove the existence of random attractors ΛH(ω) in H; Secondly, we prove the existence of random attractors ΛV (ω) in V. Then we verify regularity of the random attractors by showing that ΛH(ω) = ΛV (ω), which implies the smoothing effect of the fluids in the sense that solution becomes eventually more regular than the initial data.  
Keywordsrandom attractors,   non-Newtonian fluids,   additive noise,   Ornstein-Uhlenbeck process     
Received: 2008-12-10;
Fund:

Supported by the Fundamental Research Funds for the Central Universities (No. 2010QS04).

Corresponding Authors: Chun-xiao GUO     Email: guochunxiao1983@sina.com
Cite this article:   
.Random Attractors of Stochastic Non-Newtonian Fluids[J]  Acta Mathematicae Applicatae Sinica, English Serie, 2012,V28(1): 165-180
URL:  
http://www.applmath.com.cn/jweb_yysxxb_en/EN/10.1007/s10255-012-0132-z      或     http://www.applmath.com.cn/jweb_yysxxb_en/EN/Y2012/V28/I1/165
 
[1] Bellout, H., Bloom, F., Ne?as, J. Young measure-valued solutions for non-Newtonian incompressible viscous fluids. Commun. PDE, 19: 1763-1803 (1994)
[2] Bloom, F. Attractors of non-newtonian fluids. J. Dyn. Diff. Eqs., 7(1): 109-140 (1995)
[3] Bloom, F., Hao, W. Regularization of a non-Newtonian system in an unbounded channel: existence of a maximal compact attractor. Nonl. Anal. TMA, 43: 743-766 (2001)
[4] Chen, W. Non-Newtonian Fluids. Science Press, Beijing, 1984 (in Chinese)
[5] Crauel, H., Debussche, A., Flandoli, F. Random attractors. J. Dyn. Diff. Equ., 9(2): 307-341 (1997)
[6] Crauel, H., Flandoli, F. Attractors for random dynamical systems. Prob. Th. Rel. Fields, 100: 365-393 (1994)
[7] Da Prato, G., Debussche, A., Temam, R. Stochastic Burgers’ equation. NoDEA, 1: 389-402 (1994)
[8] Da Prato, G., Zabczyk, J. Stochastic Equations in Infinite Dimensions. Cambridge University Press, Cambridge, 1992
[9] de Bouard, A., Debussche, A. On the stochastic korteweg-de vries equation. J. Functional Analysis, 154: 215-251 (1998)
[10] de Bouard, A., Debussche, A. A stochastic nonlinear Schrödinger equation with multiplicative noise. Comm. Math. Phys., 205: 161-181 (1999)
[11] de Bouard, A., Debussche, A. The stochastic nonlinear Schrödinger equation in H1. Stochastic Analysis and Applications, 21(1): 97-126 (2003)
[12] Guo, B., Lin, G., Shang, Y. Non-Newtonian Fluids Dynamical Systems. National Defense Industry Press, 2006 (in Chinese)
[13] Krylov, N.V., Rozovsikii, B.L. Stochastic evolution equations. J. Soviet Math., 1979, 71-147. Transl., 16: 1233-1277 (1981) (in Russian)
[14] Zhao, C., Zhou, S. Pullback attractors for a non-autonomous incompressible non-Newtonian fluid. J. Diff. Equ., 238: 394-425 (2007)
[15] Zhao, C., 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)
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