Global Existence for the 3D Tropical Climate Model with Small Initial Data in ((H)over dot)1/2(R3)

The well-posedness problem is an important but challenging research topic in nonlinear partial differential equations. In this paper, we establish a global-in-time existence result of strong solutions for small initial data in terms of the ((H)over dot)(1/2)(R-3) norm on three-dimensional tropical climate model with viscosities by derive a blow-up criterion combine with energy estimates. This result can be regard as a generalization of the famous Fujita-Kato result to 3D Navier-Stokes equations.