Topological Methods in Nonlinear Analysis

Asymptotic analysis of the Navier-Stokes equations in thin domains

I. Moise, R. Temam, and M. Ziane

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Article information

Source
Topol. Methods Nonlinear Anal., Volume 10, Number 2 (1997), 249-282.

Dates
First available in Project Euclid: 19 October 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1476842206

Mathematical Reviews number (MathSciNet)
MR1634572

Zentralblatt MATH identifier
0957.35108

Citation

Moise, I.; Temam, R.; Ziane, M. Asymptotic analysis of the Navier-Stokes equations in thin domains. Topol. Methods Nonlinear Anal. 10 (1997), no. 2, 249--282. https://projecteuclid.org/euclid.tmna/1476842206


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References

  • \ref\no1A. Assemien, G. Bayada and M. Chambat, Inertial effects in the asymptotic behavior of a thin film flow , Asymptotic Anal., 9 (1994), 177–208
  • \ref\no2 L. Cattabriga, Su un problema al contorno relativo al sistema di equazioni di Stokes , Rend. Sem. Mat. Univ. Padova, 31 (1961), 308–340
  • \ref\no3 Ph. Ciarlet, Plates and junctions in elastic multi-structures , An Asymptotic Analysis, Masson, Paris and Springer-Verlag, New York (1990)
  • \ref\no4 P. Constantin and C. Foias, Navier–Stokes equations, Univ. of Chicago Press, Chicago (1988)
  • \ref\no5 H.L. Le Dret, Problèmes variationnels dans les multi-domaines: Modélisation des jonctions et applications, Masson, Paris (1991)
  • \ref\no6 J. M. Ghidaglia, Régularité des solutions de certains problèmes aux limites linéaires liés aux équations d'Euler , Comm. Partial Differential Equations, 9 \number 13 (1984), 1265–1298
  • \ref\no7 P. Grisvard, Elliptic problems in nonsmooth domains , Monographs and Studies in Mathematics, 24 , Pitman, London (1985)
  • \ref\no8 J. Hale and G. Raugel, A damped hyperbolic equation on thin domains , Trans. Amer. Math. Soc., 329 (1992), 185–219
  • \ref\no9 O. A. Ladyzhenskaya, Solution “in the large” to the boundary-value problem for the Navier–Stokes equations in two space variables , Soviet Physics. Dokl., 123 (1958), 1128–1131 \ref\no10 ––––, The mathematical theory of viscous incompressible flow, Gordon and Breach, New York (1969) \ref\no11 ––––, Some comments on my papers on the theory of attractors for abstract semigroups , Zap. Nauchn. Sem. LOMI, 182 , (Russian (1990); English translation, J. Soviet Math. 62 (1992), 101–147)
  • \ref\no12 O. A. Ladyzhenskaya and V. A. Solonnikov, On the solutions of the boundary value problems for the Navier–Stokes equations in domains with non compact boundaries , Leningrad Universitat Vestnik, 13 (1977), 39–47
  • \ref\no13 J. Leray, Etude de diverses équations intégrales et non linéaires et de quelques problèmes que pose l'hydrodynamique , J. Math. Pures Appl., 12 (1933), 1–82
  • \ref\no14 J. L. Lions, Quelques méthodes de résolution des problèmes aux limites non linéaires, Gauthier Villars, Paris (1969)
  • \ref\no15 G. Raugel and G. Sell, Equations de Navier-Stokes dans des domaines minces en dimension trois: régularité globale , C.R. Acad. Sci. Paris Sér. I Math., 309 (1989), 299–303 \ref\no16 ––––, Navier–Stokes equations on thin 3D domains. I. Global attractors and global regularity of solutions , J. Amer. Math. Society, 6 (1993), 503–568 \ref\no17 ––––, Navier–Stokes equations on thin 3D domains. II. Global regularity of spatially periodic conditions , Collège de France Proceedings, Pitman Res. Notes Math. Ser., Pitman, New York and London (1994)
  • \ref\no18 V. A. Solonnikov, On general boundary value problems for elliptic systems in the sense of Douglis–Nirenberg , I, Izv. Akad. Nauk SSSR, Ser. Mat., 28 (1964), 665–706 \moreref, II, Trudy Mat. Inst. Steklov 92 (1996), 233–297
  • \ref\no19 R. Temam, Navier–Stokes Equations, Studies in Mathematics and its Applications 2, North–Holland (1984) \ref\no20 ––––, Navier–Stokes Equations and nonlinear functional analysis, CBMS Regional Conference Series, No. 41, SIAM, Philadelphia (1995) \ref\no21 ––––, Infinite dimensional dynamical systems in mechanics and physics, Springer-Verlag, New York (1997)
  • \ref\no22 R. Temam and M. Ziane, Navier–Stokes equations in thin spherical domains , Contemporary Mathematics, AMS, to appear \ref\no23 ––––, Navier–Stokes Equations in Three–Dimensional Thin Domains with various boundary conditions , Adv. Differential Equations, 1 (1996), 499–546
  • \ref\no24 M. Ziane, On the two dimensional Navier–Stokes equations with the free boundary condition , J. Appl. Math. and Optimization, to appear
  • \ref\no25 M. Ziane, Optimal bounds on the dimension of atractors for the Navier–Stokes equations in thin spherical domains , Physica D, 105 (1997), 1–19 }