Couches d’Ekman pour les fluides tournants et la limite du système de Navier-Stokes vers celui d’Euler.

Nader Masmoudi[1]

  • [1] CEREMADE-UMR CNRS 7534, Université Paris Dauphine, Place de Lattre de Tassigny, 75775 Paris cedex 16, France

Séminaire Équations aux dérivées partielles (1998-1999)

  • Volume: 1998-1999, page 1-13

How to cite

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Masmoudi, Nader. "Couches d’Ekman pour les fluides tournants et la limite du système de Navier-Stokes vers celui d’Euler.." Séminaire Équations aux dérivées partielles 1998-1999 (1998-1999): 1-13. <http://eudml.org/doc/10966>.

@article{Masmoudi1998-1999,
affiliation = {CEREMADE-UMR CNRS 7534, Université Paris Dauphine, Place de Lattre de Tassigny, 75775 Paris cedex 16, France},
author = {Masmoudi, Nader},
journal = {Séminaire Équations aux dérivées partielles},
keywords = {vanishing parameters; half-well-prepared data},
language = {fre},
pages = {1-13},
publisher = {Centre de mathématiques Laurent Schwartz, École polytechnique},
title = {Couches d’Ekman pour les fluides tournants et la limite du système de Navier-Stokes vers celui d’Euler.},
url = {http://eudml.org/doc/10966},
volume = {1998-1999},
year = {1998-1999},
}

TY - JOUR
AU - Masmoudi, Nader
TI - Couches d’Ekman pour les fluides tournants et la limite du système de Navier-Stokes vers celui d’Euler.
JO - Séminaire Équations aux dérivées partielles
PY - 1998-1999
PB - Centre de mathématiques Laurent Schwartz, École polytechnique
VL - 1998-1999
SP - 1
EP - 13
LA - fre
KW - vanishing parameters; half-well-prepared data
UR - http://eudml.org/doc/10966
ER -

References

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  1. L.Amerio, G.Prouse : Almost-periodic functions ans functional equations. The University Series in Higher Mathematics, Van Nostrand Reinhold Company 1971  Zbl0215.15701MR275061
  2. A. Babin, A. Mahalov, B. Nicolaenko : Global splitting, integrability and regularity of 3D Euler and Navier-Stokes equations for uniformly rotating fluids.European J. Mech. B Fluids 15 (1996), no. 3, 291–300. Zbl0882.76096MR1400515
  3. A. Babin, A. Mahalov, B. Nicolaenko : Regularity and integrability of 3 D Euler and Navier-Stokes equations for rotating fluids. Asymptot. Anal. 15 (1997), no. 2, 103–150. Zbl0890.35109MR1480996
  4. C. Bardos : Existence et unicité de l’équation l’Euler en dimension deux. Journal de Math. Pures et Appliquées 40(1972), 769-790. Zbl0249.35070
  5. T. Beale, A. Bourgeois : Validity of the quasigeostrophic model for large scale flow in the atmosphere and ocean, SIAM J. Math. Anal., 25 ̲ ( 1994 ), 1023 - 1068 Zbl0811.35097MR1278890
  6. H.Bohr : Almost Periodic Functions. Chelsea Publishing Company 1947  MR20163
  7. R.E.Caflisch, M.Sammartino : Zero viscosity limit for analytic solutions of the Navier-Stokes equations on a half-space preprint 1996 MR1461106
  8. J.-Y. Chemin : A propos d’un problème de pénalisation de type antisymétrique, J. Math. Pures Appl. (9) 76 (1997), no. 9, 739–755. Zbl0896.35103
  9. T. Colin, P. Fabrie : Rotating fluid at high Rossby number driven by a surface stress : existence and convergence, preprint, 1996 Zbl1023.76593MR1751425
  10. Colin, P. Fabrie : Équations de Navier-Stokes 3 -D avec force de Coriolis et viscosité verticale évanescente. C. R. Acad. Sci. Paris Sér. I Math. 324 (1997), no. 3, 275–280. Zbl0882.76098MR1438399
  11. B. Desjardins, E. Grenier, Derivation of the quasigeostrophic potential vorticity equations. to appear in Advances in Diff. Equations. Zbl0967.76096
  12. P. Embid, A. Majda : Averaging over fast gravity waves for geophysical flows with arbitrary potential vorticity, Comm. Partial Differential Equations, 21 ̲ , (1996), 619 - 658 Zbl0849.35106MR1387463
  13. V.W. Ekman : On the influence of the earth’s rotation on ocean currents. Arkiv. Matem., Astr. Fysik, Stockholm 2 ( 11 ) 1905
  14. I. Gallagher, Un résultat de stabilité pour les solutions faibles des équations des fluides tournants, Notes aux Comptes-Rendus de l’Académie des Sciences de Paris, ( 324), Série 1, 1996, pages 183–186. Zbl0878.76081
  15. H.P.Greenspan : The theory of rotating fluids, Cambridge monographs on mechanics and applied mathematics , 1969  Zbl0182.28103
  16. E. Grenier, Oscillatory perturbations of the Navier Stokes equations. Journal de Maths Pures et Appl. 9 76 ( 1997 ), no. 6 , p. 477 - 498 Zbl0885.35090MR1465607
  17. E. Grenier, N.Masmoudi : Ekman layers of rotating fluids, the case of well prepared initial data, Comm. Partial Differential Equations , 22(5-6),(1997) 953-975 Zbl0880.35093MR1452174
  18. T.Kato : Remarks on zero viscosity limit for nonstationary Navier-Stokes flows with boundary. Zbl0559.35067
  19. T.Kato : Non-stationary flows of viscous and ideal fluids in R 3 , J.Functional Analysis 9 (1972), 296-305. Zbl0229.76018MR481652
  20. J. Leray, Essai sur le mouvement d’un liquide visqueux emplissant l’espace, Acta Matematica, 63, 1933, pages 193–248. Zbl59.0763.02
  21. J.-L. Lions, R. Temam, S. Wang : Modèles et analyse mathématiques du système Océan/Atmosphère C.R.Acad.Sci.Paris Sér. I Math 316 ̲ 1993 113 - 119 , C.R.Acad.Sci.Paris Sér. I Math 316 ̲ 1993 211 - 215 C.R.Acad.Sci.Paris Sér. I Math 318 ̲ 1994 1165 - 1171
  22. J.-L. Lions, R. Temam et S. Wang, New formulations of the primitive equations of the atmosphere and applications, Nonlinearity, 5, 1992, pages 237–288. Zbl0746.76019MR1158375
  23. J.-L. Lions, R. Temam et S. Wang, Geostrophic asympotics of the primitive equations of the atmosphere, Topological Methods in Non Linear Analysis, 4, 1994, pages 1–35. Zbl0846.35106MR1350974
  24. P.L. Lions, Mathematical Topics in Fluid Dynamics, Vol.  1 Incompressible Models, Oxford University Press 1996 Zbl0866.76002MR1422251
  25. P.L. Lions, N. Masmoudi, Incompressible limit for a viscous compressible fluid. J. Math. Pures Appl. 77 ( 1998 ), p. 585-627. Zbl0909.35101MR1628173
  26. A. Majda, T. Esteban :A two-dimensional model for quasigeostrophic flow : comparison with the two-dimensional Euler flow. Nonlinear phenomena in ocean dynamics (Los Alamos, NM, 1995). Phys. D 98 (1996), no. 2-4, 515–522. Zbl0899.76105MR1422288
  27. N. Masmoudi, The Euler limit of the Navier Stokes equations, and rotating fluids with boundary, Arch. Rational Mech. Anal142 (1998) p. 375 - 394 Zbl0915.76017MR1645962
  28. N. Masmoudi, Ekman layers of rotating fluids, the case of general initial data, to appear in Communications in Pure and Applied Mathematics . Zbl1047.76124MR1733696
  29. J. Pedlovsky : Geophysical fluid dynamics, Springer, 1979 Zbl0713.76005
  30. J. Rauch : Boundary value problems as limits of problems in all space, Séminaire Goulaouic-Schwartz, Ecole Polytechnique, exposé n.3,1978. Zbl0435.35052MR557514
  31. S. Schochet : Fast singular limits of hyperbolic PDEs. J. Diff. Equ. 114 (1994) 476 - 512 Zbl0838.35071MR1303036
  32. H.Swann, The convergence with vanishing viscosity of non-stationary Navier-Stokes flow to ideal flow in R 3 Trans. Amer. Math. Soc 157 (1971), 373-397. Zbl0218.76023MR277929

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