In this paper, we investigate the problem of fast rotating fluids between two infinite plates with Dirichlet boundary conditions and “turbulent viscosity” for general 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.
Classification : 35Q30, 35Q35, 76U05
Mots clés : Navier-Stokes equations, rotating fluids, Strichartz estimates
@article{COCV_2002__8__441_0, author = {Chemin, Jean-Yves and Desjardins, Beno\^\i t and Gallagher, Isabelle and Grenier, Emmanuel}, title = {Ekman boundary layers in rotating fluids}, journal = {ESAIM: Control, Optimisation and Calculus of Variations}, pages = {441--466}, publisher = {EDP-Sciences}, volume = {8}, year = {2002}, doi = {10.1051/cocv:2002037}, zbl = {1070.35505}, mrnumber = {1932959}, language = {en}, url = {www.numdam.org/item/COCV_2002__8__441_0/} }
Chemin, Jean-Yves; Desjardins, Benoît; Gallagher, Isabelle; Grenier, Emmanuel. Ekman boundary layers in rotating fluids. ESAIM: Control, Optimisation and Calculus of Variations, Tome 8 (2002) , pp. 441-466. doi : 10.1051/cocv:2002037. http://www.numdam.org/item/COCV_2002__8__441_0/
[1] Global regularity of 3D rotating Navier-Stokes equations for resonant domains. Indiana Univ. Math. J. 48 (1999) 1133-1176. | Zbl 0932.35160
, and ,[2] Global splitting, integrability and regularity of D Euler and Navier-Stokes equations for uniformly rotating fluids. European J. Mech. B Fluids 15 (1996) 291-300. | Zbl 0882.76096
, and ,[3] Fluids with anisotropic viscosity. Modél. Math. Anal. Numér. 34 (2000) 315-335. | Numdam | MR 1765662 | Zbl 0954.76012
, , and ,[4] Anisotropy and dispersion in rotating fluids. Preprint of Orsay University. | MR 1935994
, , and ,[5] Stability of mixed Ekman-Hartmann boundary layers. Nonlinearity 12 (1999) 181-199. | Zbl 0939.35151
, and ,[6] Applications of Schochet's methods to parabolic equations. J. Math. Pures Appl. 77 (1998) 989-1054. | Zbl 1101.35330
,[7] The theory of rotating fluids1980). | MR 639897 | Zbl 0443.76090
,[8] Oscillatory perturbations of the Navier-Stokes equations. J. Math. Pures Appl. 76 (1997) 477-498. | Zbl 0885.35090
,[9] Ekman layers of rotating fluids, the case of well prepared initial data. Comm. Partial Differential Equations 22 (1997) 953-975. | MR 1452174 | Zbl 0880.35093
and ,[10] Ekman layers of rotating fluids: The case of general initial data. Comm. Pure Appl. Math. 53 (2000) 432-483. | MR 1733696 | Zbl 1047.76124
,[11] Pedlovsky, Geophysical Fluid Dynamics. Springer-Verlag (1979). | Zbl 0429.76001