A regularity criterion for a 3D tropical climate model with damping

TL;DR

This paper establishes a regularity criterion for a 3D tropical climate model with damping, enabling the extension of local smooth solutions to global solutions, thus advancing understanding of climate system dynamics.

Contribution

It introduces a new regularity criterion for the 3D tropical climate model with damping, ensuring solutions can be extended globally in time.

Findings

Regularity criterion for the model established

Local solutions extended to global solutions

Damping terms play a key role in regularity

Abstract

In this paper we deal with the 3D tropical climate model with damping terms in the equation of the barotropic mode $u$ and in the equation of the first baroclinic mode $v$ of the velocity, and we establish a regularity criterion for this system thanks to which the local smooth solution $(u, v, \theta)$ can actually be extended globally in time.