EXISTENCE OF THE UNIFORM TRAJECTORY ATTRACTOR FOR A 3D INCOMPRESSIBLE NON-NEWTONIAN FLUID FLOW

doi:10.1016/S0252-9602(17)30126-1

数学物理学报(英文版) ›› 2018, Vol. 38 ›› Issue (1): 187-202.doi: 10.1016/S0252-9602(17)30126-1

EXISTENCE OF THE UNIFORM TRAJECTORY ATTRACTOR FOR A 3D INCOMPRESSIBLE NON-NEWTONIAN FLUID FLOW

汪承志¹, 张明书², 赵才地²

1. School of River and Ocean Engineering, Chongqing Jiaotong University, Chongqing 400074, China;
2. Department of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China

收稿日期:2016-10-20 修回日期:2017-03-24 出版日期:2018-02-25 发布日期:2018-02-25
作者简介:Chengzhi WANG,E-mail:wchzhi@126.com;Mingshu ZHANG,E-mail:450420085@qq.com;Caidi ZHAO,E-mail:zhaocaidi2013@163.com
基金资助:
Supported by NSFC (51209242, 2011BAB09B01, 11271290) and by NSF of Zhejiang Province (LY17A010011).

EXISTENCE OF THE UNIFORM TRAJECTORY ATTRACTOR FOR A 3D INCOMPRESSIBLE NON-NEWTONIAN FLUID FLOW

Chengzhi WANG¹, Mingshu ZHANG², Caidi ZHAO²

1. School of River and Ocean Engineering, Chongqing Jiaotong University, Chongqing 400074, China;
2. Department of Mathematics and Information Science, Wenzhou University, Wenzhou 325035, China

Received:2016-10-20 Revised:2017-03-24 Online:2018-02-25 Published:2018-02-25
Supported by:
Supported by NSFC (51209242, 2011BAB09B01, 11271290) and by NSF of Zhejiang Province (LY17A010011).

摘要/Abstract

摘要：

This paper studies the trajectory asymptotic behavior of a non-autonomous incompressible non-Newtonian fluid in 3D bounded domains. In appropriate topologies, the authors prove the existence of the uniform trajectory attractor for the translation semigroup acting on the united trajectory space.

关键词: incompressible non-Newtonian fluid, uniform trajectory attractor, topological space

Abstract:

Key words: incompressible non-Newtonian fluid, uniform trajectory attractor, topological space

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.

Chengzhi WANG, Mingshu ZHANG, Caidi ZHAO. EXISTENCE OF THE UNIFORM TRAJECTORY ATTRACTOR FOR A 3D INCOMPRESSIBLE NON-NEWTONIAN FLUID FLOW[J]. Acta mathematica scientia,Series B, 2018, 38(1): 187-202.

参考文献

[1] Adams R A. Sobolev Spaces. New York:Academic Press, 1975
[2] Bae H O. Existence, regularity and decay rate of solutions of non-Newtonian flow. J Math Anal Appl, 1999, 231:467-491
[3] Ball J M. Continuity properties of global attractors of generalized semiflows and the Navier-Stokes equations. J Nonl Sci, 1997, 7:475-502
[4] Bellout H, Bloom F, Nečas J. Young measure-valued solutions for non-Newtonian incompressible viscous fluids. Comm PDE, 1994, 19:1763-1803
[5] Bellout H, Bloom F. Incompressible Bipolar and Non-Newtonian Viscous Fluid Flow. New York:Springer, 2014
[6] Bloom F, Hao W. Regularization of a non-Newtonian system in an unbounded channel:existence and uniqueness of solutions. Nonlinear Anal-Theory Methods Appl, 2001, 44:281-309
[7] Bloom F, Hao W. Regularization of a non-Newtonian system in an unbounded channel:existence of a maximal compact attractor. Nonlinear Anal-Theory Methods Appl, 2001, 43:743-766
[8] Caraballo T, Langa J, Valero J. Global attractors for multivalued random dynamical systems generated by random differential inclusions with multiplicative noise. J Math Anal Appl, 2001, 260:602-622
[9] Caraballo T, Langa J, Valero J. Global attractors for multivalued random semiflows generated by random differential inclusions with additive noise. C R Acad Sci Paris Sér I, 2001, 332:131-136
[10] Caraballo T, Langa J, Melnik V, Valero J. Pullback attractors of nonautonomous and stochastic multivalued dynamical systems. Set-Valued Anal, 2003, 11:153-201
[11] Caraballo T, Kloeden P E, Rubio P M. Weak pullback attractors of setvalued processes. J Math Anal Appl, 2003, 288:692-707
[12] Chepyzhov V V, Vishik M I. Evolution equations and their trajectory attractors. J Math Pures Appl, 1997, 76:913-664
[13] Chepyzhov V V, Vishik M I. Attractors for Equations of Mathematical Physics. Providence, RI:Amer Math Soc, 2002
[14] Chepyzhov V V, Vishik M I, Zelik S V. Strong trajectory attractors for dissipative Euler equations. J Math Pures Appl, 2001, 96:395-407
[15] Dong B, Chen Z. Global attractors of two dimensional micropolar fluid flows in some unbounded domains. Appl Math Comp, 2006, 182:610-620
[16] Dong B, Chen Z. On upper and lower bounds of higher order derivatives for solutions to the micropolar fluid flows in R². J Math Anal Appl, 2007, 334:1386-1399
[17] Dong B, Jiang W. On the decay of higher order derivatives of solutions to Ladyzhenskaya model for incompressible viscous flows. Sci China Ser A:Math, 2008, 51:925-934
[18] Guo B, Guo C. The convergence for non-Newtonian fluids to Navier-Stokes equations in 3D domain. Inter J Dyna Syst Differ Equ, 2009, 2:129-138
[19] Guo B, Lin G, Shang Y. Dynamics of Non-Newtonian Fluid. Beijing:National Defence Industry Press, 2006
[20] Guo B, Zhu P. Partial regularity of suitable weak solution to the system of the incompressible nonNewtonian fluids. J Differ Equ, 2002, 178:281-297
[21] Jia Y, Zhang X, Dong B. The asymptotic behavior of solutions to three-dimensional Navier-Stokes equations with nonlinear damping. Nonlinear Anal-Real World Appl, 2011, 12:1736-1747
[22] Kapustyan A V, Valero J. Weak and strong attractors for the 3D Navier-Stokes system. J Differ Equ, 2007, 240:249-278
[23] Li Y, Zhao C. Global attractor for a non-Newtonian system in two-dimensional unbounded domains. Acta Anal Funct Appl, 2002, 4:343-349
[24] Liu G, Zhao C, Cao J. H⁴-Boundedness of pullback attractor for a 2D non-Newtonian fluid flow. Front Math China, 2013, 8:1377-1390
[25] Málek J, Nečas J, Rokyta M, R·užička M. Weak and Measure-valued Solutions to Evolutionary PDEs. New York:Champman-Hall, 1996
[26] Melnik V S, Valero J. On attractors of multi-valued semi-flows and differential inclusions. Set-Valued Anal, 1998, 6:83-111
[27] Melnik V, Valero J. On global attractors of multivalued semiprocess and nonautonomous evolution inclusions. Set-Valued Anal, 2000, 8:375-403
[28] Pokorný M. Cauchy problem for the non-Newtonian viscous incompressible fluids. Appl Math, 1996, 41:169-201
[29] Vishik M I, Chepyzhov V V. Trajectory and global attractors of three-dimensional Navier-Stokes systems. Math Notes, 2002, 77:177-193
[30] Wang Y, Zhou S. Kernel sections and uniform attractors of multi-valued semiprocesses. J Differ Equ, 2007, 232:573-622
[31] Zhao C, Li Y. H²-compact attractor for a non-Newtonian system in two-dimensional unbounded domains. Nonlinear Anal-Theory Methods Appl, 2004, 56:1091-1103
[32] Zhao C, Li Y. A note on the asymptotic smoothing effect of solutions to a non-Newtonian system in 2D unbounded domains. Nonlinear Anal-Theory Methods Appl, 2005, 60:475-483
[33] Zhao C, Zhou S, Li Y. Trajectory attractor and global attractor for a two-dimensional incompressible non-Newtonian fluid. J Math Anal Appl, 2007, 325:1350-1362
[34] Zhao C, Zhou S. Pullback attractors for nonautonomous incompressible non-Newtonian fluid. J Differ Equ, 2007, 238:394-425
[35] Zhao C, Li Y, Zhou S. Regularity of trajectory attractor and upper semicontinuity of global attractor for 2D non-Newtonian fluid. J Differ Equ, 2009, 247:2331-2363
[36] Zhao C, Zhou S, Li Y. Existence and regularity of pullback attractors for an incompressible non-Newtonian fluid with delays. Quart Appl Math, 2009, 61:503-540
[37] Zhao C. Pullback asymptotic behavior of solutions for a non-autonomous non-Newtonian fluid on 2D unbounded domains. J Math Phys, 2012, 12:1-21
[38] Zhao C. Approximation of the incompressible non-Newtonian fluid equations by the artificial compressibility method. Math Meth Appl Sci, 2013, 36:840-856
[39] Zhao C, Liu G, Wang W. Smooth pullback attractors for a non-autonomous 2D non-Newtonian fluid and their tempered behavior. J Math Fluid Mech, 2014, 16:243-262
[40] Zhao C, Kong L, Liu G, Zhao M. The trajectory attractor and its limiting behavior for the convective Brinkman-Forchheimer equations. Topol Methods Nonlinear Anal, 2014, 44:413-433
[41] Zhao C, Wu H, Li C. Trajectory attractor for a class of three-dimensional incompressible non-Newtonian fluids (in Chinese). Acta Math Sin (Chinese Ser), 2015, 58:1-12

EXISTENCE OF THE UNIFORM TRAJECTORY ATTRACTOR FOR A 3D INCOMPRESSIBLE NON-NEWTONIAN FLUID FLOW

EXISTENCE OF THE UNIFORM TRAJECTORY ATTRACTOR FOR A 3D INCOMPRESSIBLE NON-NEWTONIAN FLUID FLOW

PDF (PC)

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 1

Metrics

本文评价

推荐阅读 10