Interface boundary value problem for the Navier-Stokes equations in thin two-layer domains

Journal of Differential Equations

Volumn 208, Issue 2 SPEC. ISS., 2005, Pages 449-493

  Chueshov, Igor D ^a   Raugel, Geneviève ^b   Rekalo, Andrey M ^a  

^a V N KARAZIN KHARKIV NATIONAL UNIVERSITY   (Ukraine)

^b UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Attractors; Global strong solutions; Interface conditions; Navier Stokes equations; Spectral decomposition; Thin domains

Indexed keywords

EID: 11144325805     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.jde.2004.03.023     Document Type: Article

References (27)

1. Avrin J.D. Large-eigenvalue global existence and regularity results for the Navier-Stokes equation J. Differential Equations 127 2 1996 365-390
2. Chueshov I.D. Rekalo A.M. Long-time dynamics of reaction-diffusion equations on thin two-layer domains, Proceedings of Equadiff, 2003.
3. Chueshov I.D. Rekalo A.M. Global attractor of contact parabolic problem on thin two-layer domain, Mat. Sb. 195(1) (2004) 103-128 (in Russian); (English translation in Sbornik: Mathematics 195(1) (2004)).
4. Constantin P. Foiaş C. Navier-Stokes Equations 1988 University of Chicago Press Chicago
5. Foiaş C. Temam R. The connection between the Navier-Stokes equations, dynamical systems, and turbulence theory, Directions in Partial Differential Equations, Academic Press, New York, 1987, pp. 55-73.
6. Hale J.K. Raugel G. Reaction-diffusion equation on thin domains J. Math. Pures Appl. 71 1992 33-95
7. Hale J.K. Raugel G. A damped hyperbolic equation on thin domains Trans. Amer. Math. Soc. 329 1992 185-219
8. Hale J.K. Raugel G. Partial differential equations on thin domains, Differential Equations and Mathematical Physics (Birmingham, AL, 1990), Academic Press, Boston, MA, 1992, pp. 63-97.
9. Hu C. Temam R. Ziane M. The primitive equations on the large scale ocean under the small depth hypothesis Discrete Continuous Dynamical Systems 9 2003 97-131
10. Iftimie D. The 3D Navier-Stokes equations seen as a perturbation of the 2D Navier-Stokes equations Bull. Soc. Math. France 127 1999 473-517
11. Iftimie D. Raugel G. Some results on the Navier-Stokes equations in thin 3D domains J. Differential Equations 169 2001 281-331
12. Kato T. Perturbation Theory for Linear Operators 1966 Springer New York
13. Lions J.-L. Magenes E. Nonhomogeneous Boundary Value Problems and Applications 1972 Springer New York
14. Lions J.-L. Temam R. Wang S. Mathematical theory for the coupled atmosphere-ocean models (CAO III) J. Math. Pures Appl. 74 1995 105-163
15. Moise I. Temam R. Ziane M. Asymptotic analysis of the Navier-Stokes equations in thin domains Topol. Methods Nonlinear Anal. 10 2 1997 249-282
16. Montgomery-Smith S. Global regularity of the Navier-Stokes equation on thin three dimensional domains with periodic boundary conditions Electronic J. Differential Equations 11 1999 1-19
17. Pedlosky J. Geophysical Fluid Dynamics 2nd Edition 1987 Springer New York
18. Raugel G. Sell G. Navier-Stokes equations on thin domains. I: global attractors and global regularity of solutions J. Amer. Math. Soc. 6 1993 503-568
19. Raugel G. Sell G. Navier-Stokes equations on thin 3D domains. II. Global regularity of spatially periodic solutions, Nonlinear Partial Differential Equations and their Applications, Collège de France Seminar, Vol. XI, Longman Sci. Tech., Harlow, 1994, pp. 205-247.
20. Reed M. Simon B. Methods of Modern Mathematical Physics II 1975 Academic Press New York
21. Rekalo A. Asymptotic behaviour of solutions of nonlinear parabolic equations on thin two-layer domain Nonlinear Anal. 52 2003 1393-1410
22. Schlichting H. Boundary Layer Theory 7th Edition 1979 McGraw Hill New York
23. Sell G.R. Global attractors for the three-dimensional Navier-Stokes equations J. Dynamics Differential Equations 8 1996 1-33
24. Temam R. Navier-Stokes Equations, Revised Edition, Studies in Mathematics and its Applications 2 1979 North-Holland Amsterdam
25. Temam R. Some mathematical aspects of the GCMs Progr. Probab. 49 2001 117-138
26. Temam R. Ziane M. Navier-Stokes equations in three-dimensional thin domains with various boundary conditions Adv. in Differential Equations 1 1996 499-546
27. Temam R. Ziane M. Navier-Stokes equations in thin spherical domains Contemp. Math. AMS 209 1997 281-314