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

 Access to full text

 Full (PDF)

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., $\underline{25}$ ($1994$), $1023-1068$. 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, $\underline{21}$, (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$$76$ ($1997$), no. $6$, p. $477-498$. Zbl0885.35090MR1465607
17. E. Grenier, N.Masmoudi : Ekman layers of rotating fluids, the case of well prepared initial data, Comm. Partial Differential Equations , 22(5-6),(1997) 953-975 Zbl0880.35093MR1452174
18. T.Kato : Remarks on zero viscosity limit for nonstationary Navier-Stokes flows with boundary. Zbl0559.35067
19. T.Kato : Non-stationary flows of viscous and ideal fluids in $R^3$, J.Functional Analysis 9 (1972), 296-305. Zbl0229.76018MR481652
20. J. Leray, Essai sur le mouvement d’un liquide visqueux emplissant l’espace, Acta Matematica, 63, 1933, pages 193–248. Zbl59.0763.02
21. J.-L. Lions, R. Temam, S. Wang : Modèles et analyse mathématiques du système Océan/Atmosphère C.R.Acad.Sci.Paris Sér. I Math$\underline{316}$$1993$$113-119$, C.R.Acad.Sci.Paris Sér. I Math$\underline{316}$$1993$$211-215$C.R.Acad.Sci.Paris Sér. I Math$\underline{318}$$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