Hostname: page-component-76fb5796d-25wd4 Total loading time: 0 Render date: 2024-04-25T11:05:06.493Z Has data issue: false hasContentIssue false
  • English
  • Français

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; Isabelle.Gallagher@math.polytechnique.fr.
Emmanuel Grenier
Affiliation:
UMPA, UMR du CNRS, ENS Lyon, 46 allée d'Italie, 69364 Lyon Cedex 07, France.
Get access

Abstract

In this paper, we investigate the problem of fast rotating fluids between two infinite plates with Dirichlet boundary conditions and “turbulent viscosity” for general L2 initial data. We use dispersive effect to prove strong convergence to the solution of the bimensionnal Navier-Stokes equations modified by the 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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

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).