Global smooth solution for the 3D generalized tropical climate model with partial viscosity and damping

TL;DR

This paper proves the global existence and smoothness of solutions for a 3D generalized tropical climate model with partial viscosity and damping, under specific parameter conditions, advancing understanding of climate model mathematical properties.

Contribution

It establishes the global well-posedness and smoothness of solutions for the model with partial viscosity and damping, for certain parameter ranges, which was previously unresolved.

Findings

Global well-posedness for $eta eq4$ and $eta eq5$

Existence of smooth solutions in $H^s( ^3)$ for $s>2$

Results hold for $rac{3}{2}\, ext{and}\,4 ext{ to }5$ parameters

Abstract

The three-dimensional generalized tropical climate model with partial viscosity and damping is considered in this paper. Global well-posedness of solutions of the three-dimensional generalized tropical climate model with partial viscosity and damping is proved for $\alpha\geq\frac{3}{2}$ and $\beta\geq4$. Global smooth solution of the three-dimensional generalized tropical climate model with partial viscosity and damping is proved in $H^s(\mathbb R^3)$ $(s>2)$ for $\alpha\geq\frac{3}{2}$ and $4\leq\beta\leq5$.