Global existence and uniqueness of strong solutions to the 2D nonhomogeneous primitive equations with density-dependent viscosity

This paper is concerned with an initial-boundary value problem of the two-dimensional inhomogeneous primitive equations with density-dependent viscosity. The global well-posedness of strong solutions is established, provided the initial horizontal velocity is suitably small, that is, ∇ u_0_L^2≤η_0 for suitably small η_0>0. The initial data may contain vacuum. The proof is based on the local well-posedness and the blow-up criterion proved in , which states that if T^* is the maximal existence time of the local strong solutions (ρ,u,w,P) and T^*<∞, then sup_0≤ t更多