Revista Matemática Iberoamericana


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Volume 27, Issue 1, 2011, pp. 1–38
DOI: 10.4171/RMI/629

Published online: 2011-04-30

Global existence for the primitive equations with small anisotropic viscosity

Frédéric Charve[1] and Van-Song Ngo[2]

(1) Université Paris 12 – Val de Marne, Créteil, France
(2) Université Paris 12 – Val de Marne, Créteil, France

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).

Keywords: Primitive equations, quasi-geostrophic system, anisotropy, dispersion, Strichartz estimates.

Charve Frédéric, Ngo Van-Song: Global existence for the primitive equations with small anisotropic viscosity. Rev. Mat. Iberoamericana 27 (2011), 1-38. doi: 10.4171/RMI/629