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Ekman boundary layers in rotating fluids

Published online by Cambridge University Press:  15 August 2002

Jean-Yves Chemin ,
Benoît Desjardins ,
Isabelle Gallagher  and
Emmanuel Grenier
Jean-Yves Chemin
Affiliation:
Centre de Mathématiques de l'École Polytechnique, UMR 7640 du CNRS, 91128 Palaiseau Cedex, France;
Benoît Desjardins
Affiliation:
CEA, BP. 12, 91680 Bruyères-le-Châtel, France.
Isabelle Gallagher
Affiliation:
Centre de Mathématiques de l'École Polytechnique, UMR 7640 du CNRS, 91128 Palaiseau Cedex, France; [email protected].
Emmanuel Grenier
Affiliation:
UMPA, UMR du CNRS, ENS Lyon, 46 allée d'Italie, 69364 Lyon Cedex 07, France.
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Abstract

In this paper, we investigate the problem of fast rotatingfluids between two infinite plates with Dirichlet boundary conditions and“turbulentviscosity” for general L 2 initial data. We use dispersive effect toprove strongconvergence to the solution of the bimensionnal Navier-Stokes equationsmodified bythe Ekman pumping term.

Keywords

Navier–Stokes equationsrotating fluidsStrichartz estimates.
Type
Research Article
Information
ESAIM: Control, Optimisation and Calculus of Variations , Volume 8: A tribute to JL Lions , 2002 , pp. 441 - 466
Copyright
© EDP Sciences, SMAI, 2002

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References

Babin, A., Mahalov, A. and Nicolaenko, B., Global regularity of 3D rotating Navier-Stokes equations for resonant domains. Indiana Univ. Math. J. 48 (1999) 1133-1176.
Babin, A., Mahalov, A. and Nicolaenko, B., Global splitting, integrability and regularity of 3D Euler and Navier-Stokes equations for uniformly rotating fluids. European J. Mech. B Fluids 15 (1996) 291-300.
Chemin, J.-Y., Desjardins, B., Gallagher, I. and Grenier, E., Fluids with anisotropic viscosity. Modél. Math. Anal. Numér. 34 (2000) 315-335. CrossRef
J.-Y. Chemin, B. Desjardins, I. Gallagher and E. Grenier, Anisotropy and dispersion in rotating fluids. Preprint of Orsay University.
Desjardins, B., Dormy, E. and Grenier, E., Stability of mixed Ekman-Hartmann boundary layers. Nonlinearity 12 (1999) 181-199. CrossRef
Gallagher, I., Applications of Schochet's methods to parabolic equations. J. Math. Pures Appl. 77 (1998) 989-1054. CrossRef
H.P. Greenspan, The theory of rotating fluids, Reprint of the 1968 original. Cambridge University Press, Cambridge-New York, Cambridge Monogr. Mech. Appl. Math. (1980).
Grenier, E., Oscillatory perturbations of the Navier-Stokes equations. J. Math. Pures Appl. 76 (1997) 477-498. CrossRef
Grenier, E. and Masmoudi, N., Ekman layers of rotating fluids, the case of well prepared initial data. Comm. Partial Differential Equations 22 (1997) 953-975. CrossRef
Masmoudi, N., Ekman layers of rotating fluids: The case of general initial data. Comm. Pure Appl. Math. 53 (2000) 432-483. 3.0.CO;2-Y>CrossRef
Pedlovsky, Geophysical Fluid Dynamics. Springer-Verlag (1979).