Pullback Attractor of 2D Nonautonomous <em>g</em>-Navier-Stokes Equations With Linear Dampness

JIANG Jin-ping; HOU Yan-ren; WANG Xiao-xia

doi:10.3879/j.issn.1000-0887.2011.02.003

Volume 32 Issue 2

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2011 > 32(2): 144-157

JIANG Jin-ping, HOU Yan-ren, WANG Xiao-xia. Pullback Attractor of 2D Nonautonomous g-Navier-Stokes Equations With Linear Dampness[J]. Applied Mathematics and Mechanics, 2011, 32(2): 144-157. doi: 10.3879/j.issn.1000-0887.2011.02.003

Citation:

PDF( 686 KB)

Pullback Attractor of 2D Nonautonomous g-Navier-Stokes Equations With Linear Dampness

doi: 10.3879/j.issn.1000-0887.2011.02.003

School of Science, Centre of Computational Geoscience, Xi'an Jiaotong University, Xi'an 710049, P. R. China;
College of Mathematics and Computer Science, Yan'an University, Yan'an, Shaanxi 716000, P. R. China

Received Date: 2010-06-05
Rev Recd Date: 2011-01-05
Publish Date: 2011-02-15

Abstract

Abstract

The pullback attractors for the 2D non-autonomous g-Navier-Stokes equations with linear dampness on some unbounded domains were investigated. The existence of the pullback attractors was proved by verifying the existence of pullback D-absorbing sets with cocycle and obtaining the pullback D-asymptotic compactness. Furthermore,the estimation of the fractal dimensions for the 2Dg-Navier-Stokes equations was given.
- pullback attractor,
- g-Navier-Stokes equation,
- pullback asymptotic compactness,
- fractal dimensions,
- linear dampness

FullText(HTML)

References(26)

References

[1]	Roh J. g-Navier-Stokes equations[D]. Ph D Dissertation. Minnesota: University of Minnesota, 2001.
[2]	Roh J. Dynamics of the g-Navier-Stokes equations[J]. J Differential Equations, 2005, 211(2):452-484. doi: 10.1016/j.jde.2004.08.016
[3]	JIANG Jin-ping, HOU Yan-ren. The global attractor of g-Navier-Stokes equations with linear dampness on R2[J].Appl Math Comput, 2009, 215(3):1068-1076. doi: 10.1016/j.amc.2009.06.035
[4]	姜金平, 侯延仁. 有界区域上2D非自治g-Navier-Stokes方程的拉回吸引子[J].应用数学和力学, 2010, 31(6): 670-680.(JIANG Jin-ping, HOU Yan-ren. Pullback attractor of 2D non-autonomous g-Navier-Stokes equations on some bounded domains[J].Applied Mathematics and Mechanics(English Edition), 2010, 31(6):697-708.)
[5]	Kwak M, Kwean H, Roh J. The dimension of attractor of the 2D g-Navier-Stokes equations[J]. J Math Anal Appl, 2006, 315(2):436-461. doi: 10.1016/j.jmaa.2005.04.050
[6]	Babin A V, Vishik M I. Attractors of partial differential equations in an unbounded domain[J]. Proc Roy Soc Edinburgh Sect A, 1990, 116:221-243. doi: 10.1017/S0308210500031498
[7]	Constantin P, Foia C, Temam R. Attractor Representing Turbulent Flows[M]. Mem Amer Math Soc, 1985, 53(314):1-67.
[8]	Rosa R. The global attractor for the 2D-Navier-Stokes flow in some unbounded domain[J]. Nonlinear Analysis, Theory, Methods and Applications, 1998, 32(1):71-85. doi: 10.1016/S0362-546X(97)00453-7
[9]	Cheban D N, Duan J. Almost periodic solutions and global attractors of nonautonomous Navier-Stokes equation[J]. J Dyn Differ Equation, 2004, 16(1):1-34. doi: 10.1023/B:JODY.0000041279.25095.8a
[10]	Cheban D N. Global Attractors of Non-Autonomous Dissipative Dynamical Systems[M]. Singapore:World Scientific, 2004.
[11]	Zhong C K, Yang M H, Sun C Y. The existence of global attractors for the norm-to-weak continuous semigroup and application to the nonlinear reaction-diffusion equations[J]. J Diff Eqns, 2006, 223(2):367-399. doi: 10.1016/j.jde.2005.06.008
[12]	Raugel G, Sell G R. Navier-Stokes equations on thin 3D domains—Ⅰ: global attractors and global regularity of solutions[J].J Amer Math Soc, 1993, 6(3):503-568.
[13]	Hou Y R, Li K T. The uniform attractor for the 2D non-autonomous Navier-Stokes flow in some unbounded domain[J].Nonlinear Analysis, 2004, 58(5/6):609-630. doi: 10.1016/j.na.2004.02.031
[14]	Caraballo T, Kloeden P E, Real J. Pullback and forward attractors for a damped wave equation with delays[J]. Stochastics and Dynamics, 2004, 4(3):405-423. doi: 10.1142/S0219493704001139
[15]	Caraballo T, Real J. Attractors for 2D Navier-Stokes models with delays[J].J Differ Equation, 2004, 205(2):271-297. doi: 10.1016/j.jde.2004.04.012
[16]	Caraballo T, Kloden P E, Marin-Rubio P. Global and pullback attractor of set-valued skew product flows[J].Ann Mat, 2006, 185(20):S23-S45.
[17]	Caraballo T, Lukaszewicz G, Real J. Pullback attractors for asymptotically compact nonautonomous dynamical systems[J]. Nonlinear Anal, 2006, 64(3):484-498. doi: 10.1016/j.na.2005.03.111
[18]	Caraballo T, Real J, Chueshov I D. Pullback attractors for stochastic heat equations in materials with memory[J]. Discrote Contin Dyn Syst Ser B, 2008, 9(3):525-539. doi: 10.3934/dcdsb.2008.9.525
[19]	Kloeden P E. Pullback attractors in nonautonomous difference equations[J]. J Differ Equations Appl, 2006, 6(1): 33-52.
[20]	Kloeden P E. Pullback attractors of nonautonomous semidynamical systems[J]. Stoch Dyn, 2003, 3(1):101-112. doi: 10.1142/S0219493703000632
[21]	Song H T, Wu H Q. Pullback attractor of nonautonomous reaction-diffusion equations[J]. J Math Anal Appl, 2007, 325(2):1200-1215. doi: 10.1016/j.jmaa.2006.02.041
[22]	Temam R. Infinite-Dimensional Dynamical System in Mechanics and Physics[M]. Vol 68.Appl Math Sci. New York: Springer-Verlag,1988.
[23]	Langa J A, Lukaszewicz G, Real J. Finite fractal dimension of pullback attractor for non-autonomous 2D Navier-Stokes equations in some unbounded domains[J]. Nonlinear Anal, 2007, 66(3):735-749. doi: 10.1016/j.na.2005.12.017
[24]	Sell G R, You Y. Dynamics of Evolutionary Equations[M]. Applied Mathematical Sciences.Vol 143. New York:Springer, 2002.
[25]	Bae H, Roh J. Existence of solutions of the g-Navier-Stokes equations[J].Taiwanese J Math, 2004, 8(1):85-102.
[26]	Temam R. Navier-Stokes Equations:Theory and Numerical Analysis[M].Providence: AMS Chelsea Publishing, 2001.