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 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.
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