Ekman boundary layers in rotating fluids
Jean-Yves Chemin; Benoît Desjardins; Isabelle Gallagher; Emmanuel Grenier
ESAIM: Control, Optimisation and Calculus of Variations (2010)
- 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 (2010): 441-466. <http://eudml.org/doc/90656>.
@article{Chemin2010,
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.
},
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; Strichartz estimates},
language = {eng},
month = {3},
pages = {441-466},
publisher = {EDP Sciences},
title = {Ekman boundary layers in rotating fluids},
url = {http://eudml.org/doc/90656},
volume = {8},
year = {2010},
}
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
DA - 2010/3//
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 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.
LA - eng
KW - Navier–Stokes equations; rotating fluids; Strichartz estimates.; Navier-Stokes equations; Strichartz estimates
UR - http://eudml.org/doc/90656
ER -
References
top- 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.
- A. Babin, A. Mahalov and B. Nicolaenko, Global splitting, integrability and regularity of 3D Euler and Navier-Stokes equations for uniformly rotating fluids. European J. Mech. B Fluids15 (1996) 291-300.
- J.-Y. Chemin, B. Desjardins, I. Gallagher and E. Grenier, Fluids with anisotropic viscosity. Modél. Math. Anal. Numér.34 (2000) 315-335.
- J.-Y. Chemin, B. Desjardins, I. Gallagher and E. Grenier, Anisotropy and dispersion in rotating fluids. Preprint of Orsay University.
- B. Desjardins, E. Dormy and E. Grenier, Stability of mixed Ekman-Hartmann boundary layers. Nonlinearity12 (1999) 181-199.
- I. Gallagher, Applications of Schochet's methods to parabolic equations. J. Math. Pures Appl.77 (1998) 989-1054.
- 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).
- E. Grenier, Oscillatory perturbations of the Navier-Stokes equations. J. Math. Pures Appl.76 (1997) 477-498.
- E. Grenier and N. Masmoudi, Ekman layers of rotating fluids, the case of well prepared initial data. Comm. Partial Differential Equations22 (1997) 953-975.
- N. Masmoudi, Ekman layers of rotating fluids: The case of general initial data. Comm. Pure Appl. Math.53 (2000) 432-483.
- Pedlovsky, Geophysical Fluid Dynamics. Springer-Verlag (1979).
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