Global large solution for the tropical climate model with diffusion

TL;DR

This paper establishes the existence of global smooth solutions for a tropical climate model in two and three dimensions, even with large initial data, by focusing on a specific dissipation mechanism.

Contribution

It proves the global well-posedness of the tropical climate model with large initial data under a particular dissipation condition, which was previously unresolved.

Findings

Global smooth solutions exist for the model in 2D and 3D.

Large initial data in certain Sobolev spaces do not prevent global solutions.

The dissipation of the first baroclinic velocity component is sufficient for global regularity.

Abstract

This paper studies the d-dimensional (d=2,3) tropical climate model with only the dissipation of the first baroclinic model of the velocity ($-\eta\Delta v$). By choosing a class of special initial data $(u_0,v_0,\theta_0)$ whose $H^s(\mathbb{R}^d)$ norm can be arbitrarily large, we obtain the global smooth solution of d-dimensional tropical climate model.