# Ekman boundary layers in rotating fluids

Jean-Yves Chemin; Benoît Desjardins; Isabelle Gallagher; Emmanuel Grenier

ESAIM: Control, Optimisation and Calculus of Variations (2002)

- Volume: 8, page 441-466
- ISSN: 1292-8119

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topChemin, Jean-Yves, et al. "Ekman boundary layers in rotating fluids." ESAIM: Control, Optimisation and Calculus of Variations 8 (2002): 441-466. <http://eudml.org/doc/244759>.

@article{Chemin2002,

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 $L^2$ 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.},

author = {Chemin, Jean-Yves, Desjardins, Benoît, Gallagher, Isabelle, Grenier, Emmanuel},

journal = {ESAIM: Control, Optimisation and Calculus of Variations},

keywords = {Navier–Stokes equations; rotating fluids; Strichartz estimates; Navier-Stokes equations},

language = {eng},

pages = {441-466},

publisher = {EDP-Sciences},

title = {Ekman boundary layers in rotating fluids},

url = {http://eudml.org/doc/244759},

volume = {8},

year = {2002},

}

TY - JOUR

AU - Chemin, Jean-Yves

AU - Desjardins, Benoît

AU - Gallagher, Isabelle

AU - Grenier, Emmanuel

TI - Ekman boundary layers in rotating fluids

JO - ESAIM: Control, Optimisation and Calculus of Variations

PY - 2002

PB - EDP-Sciences

VL - 8

SP - 441

EP - 466

AB - In this paper, we investigate the problem of fast rotating fluids between two infinite plates with Dirichlet boundary conditions and “turbulent viscosity” for general $L^2$ 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.

LA - eng

KW - Navier–Stokes equations; rotating fluids; Strichartz estimates; Navier-Stokes equations

UR - http://eudml.org/doc/244759

ER -

## References

top- [1] A. Babin, A. Mahalov and B. Nicolaenko, Global regularity of 3D rotating Navier–Stokes equations for resonant domains. Indiana Univ. Math. J. 48 (1999) 1133-1176. Zbl0932.35160
- [2] A. Babin, A. Mahalov and B. Nicolaenko, Global splitting, integrability and regularity of $3$D Euler and Navier–Stokes equations for uniformly rotating fluids. European J. Mech. B Fluids 15 (1996) 291-300. Zbl0882.76096
- [3] J.-Y. Chemin, B. Desjardins, I. Gallagher and E. Grenier, Fluids with anisotropic viscosity. Modél. Math. Anal. Numér. 34 (2000) 315-335. Zbl0954.76012MR1765662
- [4] J.-Y. Chemin, B. Desjardins, I. Gallagher and E. Grenier, Anisotropy and dispersion in rotating fluids. Preprint of Orsay University. Zbl1034.35107MR1935994
- [5] B. Desjardins, E. Dormy and E. Grenier, Stability of mixed Ekman–Hartmann boundary layers. Nonlinearity 12 (1999) 181-199. Zbl0939.35151
- [6] I. Gallagher, Applications of Schochet’s methods to parabolic equations. J. Math. Pures Appl. 77 (1998) 989-1054. Zbl1101.35330
- [7] 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). Zbl0443.76090MR639897
- [8] E. Grenier, Oscillatory perturbations of the Navier–Stokes equations. J. Math. Pures Appl. 76 (1997) 477-498. Zbl0885.35090
- [9] E. Grenier and N. Masmoudi, Ekman layers of rotating fluids, the case of well prepared initial data. Comm. Partial Differential Equations 22 (1997) 953-975. Zbl0880.35093MR1452174
- [10] N. Masmoudi, Ekman layers of rotating fluids: The case of general initial data. Comm. Pure Appl. Math. 53 (2000) 432-483. Zbl1047.76124MR1733696
- [11] Pedlovsky, Geophysical Fluid Dynamics. Springer-Verlag (1979). Zbl0429.76001

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