Time decay rate of solutions to the tropical climate model equations in ℝⁿ

Abstract

This paper is devoted to study the time decay of tropical climate model. We first establish the optimal decay rates in $L^2$ of the weak solutions with large initial data in ${\mathbb{R}}^n$ and obtain the existence and uniqueness of global smooth solutions with small initial data. In addition, taking advantage of Fourier splitting method, we get the decay rates in $L^2$ for higher order derivatives of the smooth solutions with small initial data.

KEYWORDS:

• Climate model
• large time behavior
• Fourier splitting method

2010 Mathematics Subject Classifications:

• 35K55
• 35Q99
• 35A99

Acknowledgements

The authors also thank the referee for careful reading and constructive comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work is partially supported by the National Natural Science Foundation of China [grant number 71772153] and the Fundamental Research Funds for the Central Universities [grant number JBK 1805006].