Initial-boundary value problem for 2D temperature-dependent tropical climate model

TL;DR

This paper proves the global existence and uniqueness of strong solutions for a 2D temperature-dependent tropical climate model with initial-boundary conditions, using energy estimates and advanced iteration methods.

Contribution

It is the first to establish global well-posedness for the 2D tropical climate model with boundary conditions, extending previous Cauchy problem results.

Findings

Global existence and uniqueness of strong solutions

Exponential decay rates of solutions

First result on initial-boundary value problem for this model

Abstract

It is well known that the tropical climate model is an important model to describe the interaction of large scale flow fields and precipitation in the tropical atmosphere. In this paper, we address the issue of global well-posedness for 2D temperature-dependent tropical climate model in a smooth bounded domain. Through classical energy estimates and De Giorgi-Nash-Moser iteration method, we obtain the global existence and uniqueness of strong solution in classical energy spaces. Compared with Cauchy problem, we establish more delicate a priori estimates with exponential decay rates. To the best of our knowledge, this is the first result concerning the global well-posedness for the initial-boundary value problem in 2D tropical climate model.