Existence and uniqueness of local weak solution of d-dimensional tropical climate model without thermal diffusion in inhomogeneous Besov space

Abstract

This paper studies the existence and uniqueness of local weak solutions to the d-dimensional tropical climate model without thermal diffusion. We establish that, when $\alpha =\beta \ge 1$, $\eta =0$, any initial data $(u_0,v_0)\in B_{2,1}^{1+\frac{d}{2}-2\alpha }({\mathbb{R}}^d)$ and ${\theta }_0\in B_{2,1}^{1+\frac{d}{2}-\alpha }({\mathbb{R}}^d)$ yields a unique weak solution.

25 pages, accepted by SCIENTIA SINICA Mathematica (in Chinese)