Global existence for the primitive equations with small anisotropic viscosity

Abstract : 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 epsilon(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).