Global well-posedness of strong solutions to the 2D nonhomogeneous incompressible primitive equations with vacuum

Abstract

We prove the global well-posedness of the strong solution to the two-dimensional inhomogeneous incompressible primitive equations for initial data with small H12-norm, which also satisfies a natural compatibility condition. A logarithmic type Sobolev embedding inequality for the anisotropic Lx∞Lz2(Ω) norm is established to obtain the global in time a priori H1(Ω)∩W1,6(Ω) estimate of the density, which guarantee the local solution to be a global one.