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 where . 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).
Cite this article
Frédéric Charve, Van-Song Ngo, Global existence for the primitive equations with small anisotropic viscosity. Rev. Mat. Iberoam. 27 (2011), no. 1, pp. 1–38DOI 10.4171/RMI/629