On long-time asymptotic behavior for solutions to 2D temperature-dependent tropical climate model

Chaoying Li; Xiaojing Xu; Zhuan Ye

doi:10.3934/dcds.2021163

Article Contents

2022, Volume 42, Issue 3: 1535-1568. Doi: 10.3934/dcds.2021163

This issue Previous Article Strong Birkhoff ergodic theorem for subharmonic functions with irrational shift and its application to analytic quasi-periodic cocycles Next Article Quantitative destruction of invariant circles

On long-time asymptotic behavior for solutions to 2D temperature-dependent tropical climate model

1.
Department of Mathematics, Changzhou University, Changzhou 213164, Jiangsu, China
2.
School of Mathematical Sciences, Beijing Normal University, Laboratory of Mathematics and Complex Systems, Ministry of Education, Beijing 100875, China
3.
Department of Mathematics and Statistics, Jiangsu Normal University, 101 Shanghai Road, Xuzhou 221116, Jiangsu, China

^* Corresponding author: Zhuan Ye
^* Corresponding author: Zhuan Ye

Received: January 31, 2021

Revised: July 31, 2021

Early access: November 2021

Published: March 2022

Xu was partially supported by the National Natural Science Foundation of China (Grants No. 12171040, No. 11771045 and No.11871087) and the National Key R & D Programe of China(Grant No. 2020YFA0712900). Ye is supported by the National Natural Science Foundation of China (Grant No. 11701232), the Natural Science Foundation of Jiangsu Province (No. BK20170224) and the Qing Lan Project of Jiangsu Province

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Abstract

In this paper, we are concerned with the long-time asymptotic behavior of the two-dimensional temperature-dependent tropical climate model. More precisely, we obtain the sharp time-decay of the solution of the system with the general initial data belonging to an appropriate Sobolev space with negative indices. In addition, when such condition of the initial data is absent, it is shown that any spatial derivative of the positive integer $ k $-order of the solution actually decays at least at the rate of $ (1+t)^{-\frac{k}{2}} $.

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Mathematics Subject Classification: Primary: 35B40, 35Q35, 35Q86, 76D03; Secondary: 86A10.

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