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

TL;DR

This paper proves the local existence and uniqueness of weak solutions for a d-dimensional tropical climate model without thermal diffusion, using inhomogeneous Besov spaces under specific parameter conditions.

Contribution

It establishes the existence and uniqueness of solutions in Besov spaces for the tropical climate model without thermal diffusion, under certain parameter constraints.

Findings

Unique local weak solutions exist for the model.

Solutions are established in inhomogeneous Besov spaces.

Results depend on parameters nd etand initial data.

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.