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 $\alpha=\beta\geq1$, $\eta=0$, 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.