RANDOM ATTRACTOR FOR A TWO-DIMENSIONAL INCOMPRESSIBLE NON-NEWTONIAN FLUID\\ WITH MULTIPLICATIVE NOISE

doi:10.1016/S0252-9602(11)60257-9

数学物理学报(英文版) ›› 2011, Vol. 31 ›› Issue (2): 567-575.doi: 10.1016/S0252-9602(11)60257-9

RANDOM ATTRACTOR FOR A TWO-DIMENSIONAL INCOMPRESSIBLE NON-NEWTONIAN FLUID\\ WITH MULTIPLICATIVE NOISE

赵才地|李用声|周盛凡

School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan |430074, China；Department of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, China Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China

收稿日期:2009-04-02 修回日期:2009-09-07 出版日期:2011-03-20 发布日期:2011-03-20
基金资助:
Sponsored by the National NSF (10901121, 10826091, 10771074, and 10771139), NSF for Postdoctors in China (20090460952), NSF of
Zhejiang Province (Y6080077), NSF of Guangdong Province (004020077), NSF of Wenzhou University (2008YYLQ01), also by Zhejiang youth teacher training project and Wenzhou 551project

RANDOM ATTRACTOR FOR A TWO-DIMENSIONAL INCOMPRESSIBLE NON-NEWTONIAN FLUID\\ WITH MULTIPLICATIVE NOISE

ZHAO Cai-De, LI Yong-Sheng, ZHOU Sheng-Fan

School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan |430074, China；Department of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China School of Mathematical Sciences, South China University of Technology, Guangzhou 510640, China Mathematics and Science College, Shanghai Normal University, Shanghai 200234, China

Received:2009-04-02 Revised:2009-09-07 Online:2011-03-20 Published:2011-03-20
Supported by:
Sponsored by the National NSF (10901121, 10826091, 10771074, and 10771139), NSF for Postdoctors in China (20090460952), NSF of
Zhejiang Province (Y6080077), NSF of Guangdong Province (004020077), NSF of Wenzhou University (2008YYLQ01), also by Zhejiang youth teacher training project and Wenzhou 551project

摘要/Abstract

摘要：

This article proves that the random dynamical system generated by a two-dimensional incompressible non-Newtonian fluid with multiplicative noise has a global random attractor, which is a random compact set absorbing any bounded nonrandom subset of the
phase space.

关键词: Random attractor, multiplicative noise, non-Newtonian fluid

Abstract:

Key words: Random attractor, multiplicative noise, non-Newtonian fluid

中图分类号:

35B40

赵才地, 李用声, 周盛凡. RANDOM ATTRACTOR FOR A TWO-DIMENSIONAL INCOMPRESSIBLE NON-NEWTONIAN FLUID\\ WITH MULTIPLICATIVE NOISE[J]. 数学物理学报(英文版), 2011, 31(2): 567-575.

ZHAO Cai-De, LI Yong-Sheng, ZHOU Sheng-Fan. RANDOM ATTRACTOR FOR A TWO-DIMENSIONAL INCOMPRESSIBLE NON-NEWTONIAN FLUID\\ WITH MULTIPLICATIVE NOISE[J]. Acta mathematica scientia,Series B, 2011, 31(2): 567-575.

参考文献

[1] Arnold A. Random Dynamical Systems. Berlin: Springer, 1998

[2] Bloom F, Hao W. Regularization of a non-Newtonian system in an unbounded channel:Existence and uniqueness of solutions. Nonl Anal, 2001, 44: 281--309

[3] Bloom F, Hao W. Regularization of a non-Newtonian system in an unbounded channel:Existence of a maximal compact attractor. Nonl Anal, 2001, 43: 743--766

[4] Bates P W, Lu K N, Wang B X. Random attractors for stochastic reaction-diffusion equations on unbounded domains. J Differential equations, 2009, 246: 845--869

{
[5] Crauel H, Flandoli F. Attractors for random dynamical systems. Probability and Related Fields, 1994, 100: 365--393

[6] Crauel H. Random point attractors versus random set attractors. J London Math Soc, 2002, 63: 413--427

[7] Crauel H, Flandoli F. Hausdorff dimension of invariant sets for random dynamical systems. J Dyn Diff Equations, 1998, 10: 449--474

[8] Crauel H A, Debussche F. Flandoli, Random Attractors. J Dyn Diff Equations, 1997, 9: 307--341

[9] Caraballo T, Lu K N. Attractors of stochastic lattice dynamical systems with a multiplicative noise. Front Math China, 2008, 3: 317--335

[10] Debussche A. On the finite dimensionality of random attractors. Stochastic Anal Appl, 1997, 15: 473--492

[11] Debussche A. Hausdorff dimension of a random invariant set. J Math Pure Appl, 1998, 77: 967--988

[12] Dong B Q, Li Y S. Large time behavior to the system of incompressible non-Newtonian fluids in R². J Math Anal Appl, 2004, 298: 667--676

[13] Dong B Q, Chen Z M. Time decay rates of non-Newtonian flows in R². J Math Anal Appl, 2006, 324: 820--833

[14] Guo B L, Zhu P C. Partial regularity of suitable weak solution to the system of the incompressible non-Newtonian fluids. J Differential Equations, 2002, 178: 281--297

[15] Guo B L, Lin G G, Shang Y D. Dynamics of Non-Newtonian fluid. Beijing: National Defence Industry Press, 2006

[16] Ladyzhenskaya O. New equations for the description of the viscous incompressible fluids and solvability in large of the boundary value problems for them//Boundary Value Problems of Mathematical Physics. AMS, Providence, RI, 1970

[17] Màlek J, Ne\v{c}as J, Rokyta M, R\.{u}\v{z}i\v{c}k M. Weak and Measure-valued Solutions to Evolutionary PDE. New York: Champman-Hall, 1996

[18] Pokorn\'{y} M. Cauchy problem for the non-Newtonian viscous incompressible fluids. Appl Math, 1996, 41: 169--201

[19] Schmalfuss B. The stochastic attractor of the stochastic Lorenz system. Z Angew Math Phy, 1997, 48: 951--975

[20] Temam R. Infinite Dimensional Dynamical Systems in Mechanics and Physics. Berlin: Springer, 1997

[21] Zhao C D, Li Y S. H²-compact attractor for a non-Newtonian system in two-dimensional unbounded domains. Nonl Anal, 2004, 7: 1091--1103

[22] Zhao C D, Zhou S F. L²-compact uniform attractors for a nonautonomous incompressible non-Newtonian fluid with locally uniformly integrable external forces in distribution space. J Math Phy, 2007, 48: 1--12

[23] Zhao C D, Zhou S F. Pullback attractors for a non-autonomous incompressible non-Newtonian fluid. J Differential Equations, 2007, 238: 394--425

[24] Zhao C D, Zhou S F. Pullback trajectory attractors for evolution equations and application to 3D incompressible non-Newtonian fluid.
Nonlinearity, 2008, 21: 1691--1717

[25] Zhao C D, Zhou S F. Sufficient conditions for the existence of global random attractors for stochastic lattice dynamical systems
and applications. J Math Anal Appl, 2009, 354: 78--95

[26] Zhao C D, Li Y S, Zhou S F. Regularity of trajectory attractor and upper semicontinuity of global attractor for a 2D non-Newtonian fluid. J Differential Equations, 2009, 247: 2331--2363

[27] Zhao C D, Zhou S F, Li Y S. Existence and regularity of pullback attractors for an incompressible non-Newtonian fluid with delays. Quar Appl Math, 2009, 67: 503--540

RANDOM ATTRACTOR FOR A TWO-DIMENSIONAL INCOMPRESSIBLE NON-NEWTONIAN FLUID\\ WITH MULTIPLICATIVE NOISE

RANDOM ATTRACTOR FOR A TWO-DIMENSIONAL INCOMPRESSIBLE NON-NEWTONIAN FLUID\\ WITH MULTIPLICATIVE NOISE

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 13

Metrics

本文评价

推荐阅读 0

[1]	Huijuan ZHU, Xiaojun LI, Yanjiao LI. EXPONENTIAL STABILITY OF ATTRACTOR FOR RANDOM REACTION-DIFFUSION EQUATION DRIVEN BY NONLINEAR COLORED NOISE ON ℝ^N[J]. 数学物理学报(英文版), 2025, 45(4): 1567-1596.
[2]	Tao Yan, Lu Zhang, Aihong Zou, Ji Shu. DYNAMICS OF THE STOCHASTIC $g$-NAVIER-STOKES EQUATIONS DRIVEN BY NONLINEAR NOISE^*[J]. 数学物理学报(英文版), 2023, 43(5): 2108-2120.
[3]	赵才地, 林泽瀚, T. Tachim MEDJO. GEVREY CLASS REGULARITY FOR THE GLOBAL ATTRACTOR OF A TWO-DIMENSIONAL NON-NEWTONIAN FLUID[J]. 数学物理学报(英文版), 2022, 42(1): 265-282.
[4]	赵文强, 张一进. UPPER SEMI-CONTINUITY OF RANDOM ATTRACTORS FOR A NON-AUTONOMOUS DYNAMICAL SYSTEM WITH A WEAK CONVERGENCE CONDITION[J]. 数学物理学报(英文版), 2020, 40(4): 921-933.
[5]	胡耀忠, Khoa LÊ. JOINT HÖLDER CONTINUITY OF PARABOLIC ANDERSON MODEL[J]. 数学物理学报(英文版), 2019, 39(3): 764-780.
[6]	郭闪闪, 谭忠. ON INTEGRABILITY UP TO THE BOUNDARY OF THE WEAK SOLUTIONS TO A NON-NEWTONIAN FLUID[J]. 数学物理学报(英文版), 2019, 39(2): 420-428.
[7]	潘洁, 方莉, 郭真华. STABILITY OF BOUNDARY LAYER TO AN OUTFLOW PROBLEM FOR A COMPRESSIBLE NON-NEWTONIAN FLUID IN THE HALF SPACE[J]. 数学物理学报(英文版), 2019, 39(1): 259-283.
[8]	汪承志, 张明书, 赵才地. EXISTENCE OF THE UNIFORM TRAJECTORY ATTRACTOR FOR A 3D INCOMPRESSIBLE NON-NEWTONIAN FLUID FLOW[J]. 数学物理学报(英文版), 2018, 38(1): 187-202.
[9]	赵文强. REGULARITY OF RANDOM ATTRACTORS FOR A STOCHASTIC DEGENERATE PARABOLIC EQUATIONS DRIVEN BY MULTIPLICATIVE NOISE[J]. 数学物理学报(英文版), 2016, 36(2): 409-427.
[10]	方莉\|李自来. ON THE EXISTENCE OF LOCAL CLASSICAL SOLUTION FOR A CLASS OF ONE-DIMENSIONAL COMPRESSIBLE NON-NEWTONIAN FLUIDS[J]. 数学物理学报(英文版), 2015, 35(1): 157-181.
[11]	赵才地, 贾晓琳, 杨新波. UNIFORM ATTRACTOR FOR NONAUTONOMOUS INCOMPRESSIBLE NON-NEWTONIAN FLUID WITH A NEW CLASS OF EXTERNAL FORCES[J]. 数学物理学报(英文版), 2011, 31(5): 1803-1812.
[12]	郭柏灵, 郭春晓, 蒲学科. RANDOM ATTRACTORS FOR A STOCHASTIC HYDRODYNAMICAL EQUATION IN HEISENBERG PARAMAGNET[J]. 数学物理学报(英文版), 2011, 31(2): 529-540.
[13]	黎育红; Zdzislaw Brzezniak; 周建中. CONCEPTUAL ANALYSIS AND RANDOM ATTRACTOR FOR DISSIPATIVE RANDOM DYNAMICAL SYSTEMS[J]. 数学物理学报(英文版), 2008, 28(2): 253-268.