Some Results on the Navier-Stokes Equations in Thin 3D Domains

Journal of Differential Equations

Volumn 169, Issue 2, 2001, Pages 281-331

  Iftimie, Dragoş ^a   Raugel, Geneviève ^b  

^a UNIVERSITÉ DE RENNES 1   (France)

^b UNIVERSITÉ PARIS SUD   (France)

Author keywords

Global existence; Navier Stokes equations; Sobolev embedding; Thin domain

Indexed keywords

EID: 0035915866     PISSN: 00220396     EISSN: None     Source Type: Journal    
DOI: 10.1006/jdeq.2000.3900     Document Type: Article

References (29)

1. Avrin J.D. Large-eigenvalue global existence and regularity results for the Navier-Stokes equation. J. Differential Equations. 127:1996;365-390.
2. H. Bahouri, and, I. Gallagher, Paraproduit sur le groupe de Heisenberg et applications, Revista Matematica Iberoamericana, to appear.
3. Bergh J., Löfström J. Interpolation Spaces. An Introduction. 1976;Springer-Verlag, Berlin.
4. Cannone M. Diderot, . Ondelettes, Paraproduits et Navier-Stokes. 1995;Arts et Sciences.
5. Constantin P., Foiaş C. Navier-Stokes Equations. 1988;University of Chicago Press, Chicago.
6. Danchin R. Poches de tourbillon visqueuses. J. Math. Pures Appl. 76:1997;609-647.
7. Dauge M. Stationary Stokes and Navier-Stokes systems on two- or three-dimensional domains with corners. Part I: Linearized equations. SIAM J. Math. Anal. 20:1989;74-97.
8. Fujita H., Kato T. On the Navier-Stokes initial value problem. I. Arch. Rational Mech. Anal. 16:1964;269-315.
9. Fujita H., Morimoto H. On fractional powers of the Stokes operator. Proc. Japan Acad. 46:1970;1141-1143.
10. Gallagher I. The tridimensional Navier-Stokes equations with almost bidimensional data: stability, uniqueness, and life span. Internat. Math. Res. Notices. 18:1997;919-935.
11. Grisvard P. Caractérisation de quelques espaces d'interpolation. Arch. Rational Mech. Anal. 25:1967;40-63.
12. Hale J. K., Raugel G. A damped hyperbolic equation on thin domains. Trans. Amer. Math. Soc. 329:1992;185-219.
13. Hale J. K., Raugel G. Partial differential equations on thin domains. Differential Equations and Mathematical Physics, Birmingham, AL, 1990. 1992;Academic Press, Boston. p. 63-97.
14. Hale J. K., Raugel G. Reaction-diffusion equation on thin domains. J. Math. Pures Appl. 71:1992;33-95.
15. 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.
16. Johnsen J. Pointwise multiplication of Besov and Triebel-Lizorkin spaces. Math. Nachr. 175:1995;85-133.
17. Ladyzhenskaya O. A. The Mathematical Theory of Viscous Incompressible Flow. 1969;Gordon and Breach, New York.
18. Leray J. Sur le mouvement d'un liquide visqueux emplissant l'espace. Acta Math. 63:1934;193-248.
19. Lions J.-L. Quelques méthodes de résolution des problèmes aux limites non linéaires. 1969;Gauthier Villars, Paris.
20. Lions J.-L., Magenes E. Problèmes aux limites non homogènes et applications. 1968;Dunod, Paris.
21. J. E. Marsden, T. S. Ratiu, and, G. Raugel, The Euler equations on thin domains, preprint.
22. Moise I., Temam R., Ziane M. Asymptotic analysis of the Navier-Stokes equations in thin domains. Topol. Methods Nonlinear Anal. 10:1997;249-282.
23. 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.
24. Raugel G., Sell G. R. Navier-Stokes equations on thin 3D domains. I. Global attractors and global regularity of solutions. J. Amer. Math. Soc. 6:1993;503-568.
25. Raugel G., Sell G. R. 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. XI:1994;Longman, Harlow. p. 205-247.
26. Temam R. Navier-Stokes Equations. 1984;North-Holland, Amsterdam.
27. Temam R., Ziane M. Navier-Stokes equations in three-dimensional thin domains with various boundary conditions. Adv. Differential Equations. 1:1996;499-546.
28. Temam R., Ziane M. Navier-Stokes equations in thin spherical domains. Contemp. Math. 209:1997;281-314.
29. von Wahl W. The Equations of Navier-Stokes and Abstract Parabolic Equations. 1985;Friedr. Vieweg, Braunschweig.