Global Existence for the 3D Tropical Climate Model with Small Initial Data in H ˙ 1 / 2 ℝ 3 ∗

Abstract

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 ˙ 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.