The uniform attractor for the 2D non-autonomous Navier-Stokes flow in some unbounded domain

Nonlinear Analysis, Theory, Methods and Applications

Volumn 58, Issue 5-6, 2004, Pages 609-630

  Hou, Yanren ^a   Li, Kaitai ^a  

^a XI'AN JIAOTONG UNIVERSITY   (China)

Author keywords

Hausdorff dimension; Navier Stokes equations; Non autonomous systems; Uniform attractors

Indexed keywords

BOUNDARY VALUE PROBLEMS; COMPUTATIONAL COMPLEXITY; DIFFERENTIAL EQUATIONS; MATHEMATICAL OPERATORS; PROBLEM SOLVING; VISCOUS FLOW;

ENERGY EQUATION; HAUSDEFF DIMENSION; NON-AUTONOMOUS SYSTEMS; UNIFORM ATTRACTORS;

NAVIER STOKES EQUATIONS;

EID: 3242733061     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2004.02.031     Document Type: Article

References (23)

1. Abergel F. Attractors for a Navier-Stokes flow in an unbounded domain. Math. Modelling Numer. Anal. 23:1989;359-370.
2. Babin A.V. The attractor of a Navier-Stokes system in an unbounded channel-like domain. J. Dynam. Differential Equations. 4:1992;555-584.
3. Babin A.V., Vishik V.B. Attractors of evolutionary partial differential equations and estimates of their attractors. Russian Math. Surveys. 38:1983;151-213. (English translation).
4. J. Ball, A proof of the existence of global attractors for damped semilinear wave equations, cited in [11].
5. Constantin P., Foias C. Global Lyapunov exponents, Kaplan-Yorke formulas and the dimension of the attractor for the 2D Navier-Stokes equations. Comm. Pure Appl. Math. XXXVIII:1985;1-27.
6. Constantin P., Foias C., Manley O., Temam R. Determing modes and fractal dimension of turbulent flows. J. Fluid Mech. 150:1988;427-440.
7. Chepyzhov V.V., Efendiev M.A. Hausdorff dimension estimation for attractors of non-autonomous dynamical systems in unbounded domains. An Example Comm. Pure Appl. Math. LIII:2000;647-665.
8. Chepyzhov V.V., Vishik M.I. Attractors of non-autonomous dynamical systems and their dimension. J. Math. Pures Appl. 73:1994;279-333.
9. Foias C., Temam R. Some analytic and geometric properties of the solutions of the evolution Navier-Stokes equations. J. Math. Pures Appl. 58:1979;334-368.
10. Ghidaglia J.M. Weakly damped forced Korteweg-de Vries equations behave as a finite dimensional dynamical system in the long time. J. Differential Equations. 74:1988;369-390.
11. Ghidaglia J.M. A note on the strong convergence towards attractors for damped forced KdV equations. J. Differential Equations. 110:1994;356-359.
12. Ghidaglia J.M., Marion M., Temam R. Generalizations of the Sobolev-Lieb-Thirring inequalities and application to the dimension of the attractor. Differential Integral Equations. 1:1988;1-21.
13. Hale J.K. Asymptotic Behavior of Dissipative Systems. Mathematical Surveys and Monographs. Vol. 25:1988;American Mathematical Society, Providence, RI.
14. O. Ladyzhenskaya, On the dynamical system generated by the Navier-Stokes equations, Z. Nauch. Semin. LOMI 27:91-114. 1972 (English translation in J. Sov. Math. 1975, 3(4)).
15. O. Ladyzhenskaya, On the dynamical system generated by the Navier-Stokes equations, Z. Nauch. Semin. LOMI 27:91-114. 1972 (English translation in J. Sov. Math. 1975, 3(4)).
16. Moise I., Rosa R., Wang X. Attractors for non-compact semigroups via energy equations. Nonlinearity. 11:1998;1369-1393.
17. Moise I., Rosa R., Wang X. Attractors for noncompact non-autonomous systems via energy equations. Discrete Continuous Dynam. Systems. 10:2004;473-496.
18. Rosa R. The global attractor for the 2D Navier-Stokes flow on some unbounded domains. Nonlinear Anal. TMA. 32:1998;71-85.
19. R. Temam, Navier-Stokes equations and nonlinear functional analysis, in: CBMS-NSF Regional Conference Series in Applied Mathematics, SIAM, Philadelphia, 1983.
20. Temam R. Navier-Stokes Equations, Theory and Numerical Analysis. 3rd Edition:1984;North-Holland, Amsterdam.
21. Temam R. Infinite Dimensional Dynamical Systems in Mechanics and Physics. Applied Mathematical Sciences. Vol. 68:1988;Springer, New York.
22. Wang B.X. Attractors for reaction-diffusion equations in unbounded domains. Physica D. 128:1999;41-52.
23. Wang X. An energy equation for the weakly damped driven nonlinear Schrödinger equations and its applications. Physica D. 88:1995;167-175.