无界区域上具线性阻尼的二维 Navier-Stokes 方程的拉回吸引子

PDF (PC)

Pullback Attractors for Non-autonomous 2D Navier-Stokes Equations with Linear Dampness in Some Unbounded Domains

Abstract

References

Metrics

Abstract

Cite this article

share this article

References

Related Articles 15

Metrics

Comments

Recommended 10

Abstract:

In this paper, the concept of pullback asymptotically compact non-autonomous dynamical system is firstly introduced. Then, a result ensuring the existence of a pullback attractor for a non-autonomous dynamical system is given. Finally, the existence of a pullback attractor for a non-autonomous 2D Navier-Stokes equation with linear dampness in some unbounded domains is proved. Moreover, the upper bounds of Fractal dimension of the pullback attractor is estimated.

Key words: Asymptotic compactness, Process, Non-autonomous, Linear dampness, Pullback attractor

CLC Number:

35B41

WANG Xiao-Hu, LI Shu-Yong. Pullback Attractors for Non-autonomous 2D Navier-Stokes Equations with Linear Dampness in Some Unbounded Domains[J].Acta mathematica scientia,Series A, 2009, 29(4): 873-881.

Trendmd

[1] Constantin P, Foias C. Navier Stokes Equations. Chicago: The University of Chicago Press, 1988

[2] Robinson J C. Infinite Dimensional Dynamical Systems. Cambridge: Cambridge University Press, 2001

[3] Temam R. Navier-Stokes Equations, Theory and Numerical Analysis. Amsterdam: North Holland, 1979

[4] Temam R. Infinite Dimensional Dynamical Systems in Mechanics and Physics. New York: Springer-Verlag, 2000

[5] Ladyzhenskaya O. On the dynamical system generated by the Navier-Stokes equations. Z Nauch Semin LOMI, 1972, 27: 91--114

[6] Foias C, Temam R. Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations. J Math Pures Appl, 1979, 58: 334--368

[7] Abergel F. Attractors for a Navier-Stokes flow in an unbounded domain. Math Modeling Numer Anal, 1998, 23: 359--370

[8] Babin A V. The attractor of a Navier-Stokes system in an unbounded channel-like domain. J Dynam Differential Equations, 1992, 4: 555--584

[9] Rosa R. The global attractor for the 2D Navier-Stokes flow on some unbounded domains. Nonlinear Anal TMA, 1998, 32: 71--85

[10] Ball J M. Global attractors for damped semi-linear wave equations. Discrete Contin Dynam Systems, 2004, 10 (1/2): 31--52

[11] Ghidaglia J M. Weakly damped forced Korteweg-de Vries equations behave as a finite dimensional dynamical system in the long time. J Differential Equations, 1988, 74: 369--390

[12] Ghidaglia J M. A note on the strong convergence towards attractors for damped forced KdV equations. J Differential Equations, 1994, 110 : 356--359

[13] Wang B X. An energy equation for the weakly damped driven nonlinear Schr"odinger equations and its applications. Physica D, 1995, 88: 167--175

[14] Chepyzhov V V , Vishik M I. Attractors of non-autonomous dynamical systems and their dimension. J Math Pures Appl, 1994, 73: 279--333

[15] Caraballo T, Langa J A, Robinson J C. Stability and random attractor for a reaction-diffusion equation with multiplicative noise. Discrete contin Dyn Syst, 2000, 6 (4): 875--892

[16] Caraballo T, Langa J A. On the upper semi-continuity of cocycle attractors for non-autonomous and random dynamical systems. Dynam Contin Discrete Impuls Systems A, 2003, 10: 491--514

[17] Kloeden P E. A Lyapunov function for pullback attractors of non-autonomous differential equations. Electron J Differ Equ Conf, 2000, 5： 91--102

[18] Kloeden P E, Schmalfuss B. Asymptotic behaviour of non-autonomous difference inclusions. Systems and Control Lett, 1998, 3: 275--280

[19] Hou Y, Li K. The uniform attractor for the 2D non-autonomous Navier-Stokes flow in some unbounded domains. Nonlinear Anal, 2004, 58(5/6): 609--630

[20] Lukaszewicz G, Sadowski W. Uniform attractor for 2D magneto-micropolar fluid flow in some unbounded domains. Z Angew Math Phys, 2004, 55: 1--11

[21] Moise I, Rosa R, Wang X. Attractors for noncompact non-autonomous systems via energy equations. Discrete Cont Dynam Syst, 2004, 10(1/2): 473--496

[22] Caraballo T, Lukaszewicz G, Real J. Pullback attractors for asymptotically compact nonautonomous dynamical systems. Nonlinear Anal, 2006, 64(3): 484--498

[23] Langa J A, Lukaszewicz G, Real J. Fintie fractal dimension of pullback attractor for non-autonomous 2D Navier-Stokes equations in some unbounded domains. Nonlinear Anal, 2007, 66: 735--749

[24] 丁夏畦, 吴永辉. 二维全平面上具线性阻尼Navier-Stokes方程组解的有限维行为. 应用数学学报, 1997, 20(4): 509--519

[25] 赵春山, 李开泰. 二维全空间上线性阻尼Navier-Stokes 方程的全局吸引子及其维数估计. 应用数学学报, 2000, 23(1): 90--98

Viewed

Full text

	From	local

	Times	16
	Rate	100%

Abstract

Just accepted	Online first	Issue

0	0	55

	From	Others

	Times	55
	Rate	100%

Cited

Web of Science	Crossref	ScienceDirect	Search for Citations in Google Scholar >>


This page requires you have already subscribed to WoS.

Shared

Discussed

Just accepted

Online first

Just accepted

Online first

[1]	Li Dingshi, Fan Yingfei. Random Attractors for the Stochastic Nonclassical Diffusion Equation on Unbounded Domains [J]. Acta mathematica scientia,Series A, 2017, 37(1): 158-172.
[2]	Wang Yonghai, Qin Yuming. Upper Semicontinuity of Pullback Attractors for Nonclassical Diffusion Equations in H₀¹(Ω) [J]. Acta mathematica scientia,Series A, 2016, 36(5): 946-957.
[3]	Hou Zhenting, Ma Yi, Liu Lu. Estimating Parameters of Stationary Distribution Using Forward Equation [J]. Acta mathematica scientia,Series A, 2016, 36(5): 997-1009.
[4]	Yang Xinguang, Zhao Mingxia, Hou Wei. Upper Semi-Continuity of Pullback Attractors for the 2D Non-Autonomous Navier-Stokes Equations with Weak Damping [J]. Acta mathematica scientia,Series A, 2016, 36(4): 722-739.
[5]	Wang Weigang, Yang Guangyu, Gao Zhenlong. Convergence of Branching Process in Varying Environments when All Moments Being Finite [J]. Acta mathematica scientia,Series A, 2016, 36(2): 353-361.
[6]	Lan Shaojun, Tang Yinghui. Analysis of the Departure Process for Geo/G/1 Discrete-Time Queue with Single Server Vacation and Min-Policy [J]. Acta mathematica scientia,Series A, 2016, 36(2): 380-392.
[7]	Sun Hongyan, Yao Yanan. Asymptotic Behavior of the Local Time for the Symmetric Random Walk with Stay [J]. Acta mathematica scientia,Series A, 2015, 35(6): 1180-1189.
[8]	Zhang Lina, Li Junping, Geng Shifeng. The Stability Property of Generalized Nonlinear Markov Branching Models with Resurrection [J]. Acta mathematica scientia,Series A, 2015, 35(6): 1190-1206.
[9]	Qiu Dehua, Chen Pingyan. large Convergence for Moving Average Processes Under END Set-up [J]. Acta mathematica scientia,Series A, 2015, 35(4): 756-768.
[10]	XIAO Jian-Zhong, YAN Jie, ZHU Xing-Hua. Explicit, Implicit and Viscosity Iterations for Nonexpansive Cosine Families in Hilbert Spaces [J]. Acta mathematica scientia,Series A, 2014, 34(6): 1518-1531.
[11]	WANG Bin. Phase Transition in A Random Graph Process with Preferential Deletion and Limiting on Vertices [J]. Acta mathematica scientia,Series A, 2014, 34(6): 1554-1577.
[12]	YANG Xin-Guang, WANG Hong-Jun, LI Jun-Tao. Uniform Attractors for the 2D Non-Autonomous Navier-Stokes Equation with Weak Damping [J]. Acta mathematica scientia,Series A, 2014, 34(4): 828-840.
[13]	ZHANG Shui-Li, ZHANG Shao-Yi. he Ergodicity of Jump Processes on General State Space [J]. Acta mathematica scientia,Series A, 2014, 34(4): 859-878.
[14]	LV Xue-Bin, DAI Wan-Yang. Stochastic Integration for Fractional L\'{e}vy Processes and Stochastic Differential Equations Driven by Fractional L\'{e}vy Noises [J]. Acta mathematica scientia,Series A, 2013, 33(6): 1022-1034.
[15]	TANG Feng-Qin, LI Ze-Hui, CHEN Jin-Yuan. The Precise Large Deviations for a Risk Model Based on the Policy Entrance Process [J]. Acta mathematica scientia,Series A, 2011, 31(3): 737-751.