JournalsrmiVol. 27, No. 1pp. 1–38

Global existence for the primitive equations with small anisotropic viscosity

  • Frédéric Charve

    Université Paris 12 – Val de Marne, Créteil, France
  • Van-Song Ngo

    Université Paris 12 – Val de Marne, Créteil, France
Global existence for the primitive equations with small anisotropic viscosity cover
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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 εα\varepsilon^\alpha where 0<α<α00 < \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).

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. 1–38

DOI 10.4171/RMI/629