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European Mathematical Society Publishing House
2016-09-19 17:05:46
Revista Matemática Iberoamericana
Rev. Mat. Iberoamericana
RMI
0213-2230
2235-0616
General
10.4171/RMI
http://www.ems-ph.org/doi/10.4171/RMI
subscribers
European Mathematical Society Publishing House
Zuerich, Switzerland
© European Mathematical Society (from 2012)
27
2011
1
Global existence for the primitive equations with small anisotropic viscosity
Frédéric
Charve
Université Paris 12 – Val de Marne, CRÉTEIL CEDEX, FRANCE
Van-Song
Ngo
Université Paris 12 – Val de Marne, CRÉTEIL CEDEX, FRANCE
Primitive equations, quasi-geostrophic system, anisotropy, dispersion, Strichartz estimates.
In this paper, we consider the primitive equations with zero vertical viscosity, zero vertical thermal diffusivity, and the horizontal viscosity and horizontal thermal diffusivity of size $\varepsilon^\alpha$ where $0 < \alpha < \alpha_0$. We prove the global existence of a unique strong solution for large data provided that the Rossby number is small enough (the rotation and the vertical stratification are large).
Partial differential equations
Fluid mechanics
General
1
38
10.4171/RMI/629
http://www.ems-ph.org/doi/10.4171/RMI/629