# Global regularity of 2D tropical climate model with zero thermal diffusion

## TL;DR

This paper proves the global regularity of a 2D tropical climate model with fractional dissipation, including cases with no dissipation, extending results to higher dimensions.

## Contribution

It establishes new global regularity results for the 2D tropical climate model with fractional dissipation, including the zero dissipation case and higher-dimensional extensions.

## Key findings

- Global regularity holds for $ ext{alpha}+ ext{beta} ext{geq}2$ with $1< ext{alpha}<2$.
- Global regularity achieved even with no dissipation at a logarithmically supercritical level.
- Results extend to higher-dimensional cases.

## Abstract

This article studies the global regularity problem of the two-dimensional zero thermal diffusion tropical climate model with fractional dissipation, given by $(-\Delta)^{\alpha}u$ in the barotropic mode equation and by $(-\Delta)^{\beta}v$ in the first baroclinic mode of the vector velocity equation. More precisely, we show that the global regularity result holds true as long as $\alpha+\beta\geq2$ with $1<\alpha<2$. In addition, with no dissipation from both the temperature and the first baroclinic mode of the vector velocity, we also establish the global regularity result with the dissipation strength at the logarithmically supercritical level. Finally, our arguments can be extended to obtain the corresponding global regularity results of the higher dimensional cases.