Global well-posedness and large time decay for the d-dimensional tropical climate model

Zhaoxia Li; Lihua Deng; Haifeng Shang; Zhaoxia Li; Lihua Deng; Haifeng Shang

doi:10.3934/math.2021330

AIMS Mathematics

2021, Volume 6, Issue 6: 5581-5595. doi: 10.3934/math.2021330

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Research article

Global well-posedness and large time decay for the d-dimensional tropical climate model

School of Mathematics and Information Science, Henan Polytechnic University, Jiaozuo, Henan 454000, China

Received: 20 January 2021 Accepted: 15 March 2021 Published: 22 March 2021
MSC : 35Q35, 35B40, 76D03

This paper investigates the Cauchy problem on the d-dimensional tropical climate model with fractional hyperviscosity. We establish the small data global well-posedness of solutions to this model with supercritical dissipation. Furthermore, we study the asymptotic stability of these global solutions and obtain the optimal decay rates by using energy method and the method of bootstrapping argument.
- d-dimensional (dD) tropical climate model,
- global well-posedness,
- temporal decay
Citation: Zhaoxia Li, Lihua Deng, Haifeng Shang. Global well-posedness and large time decay for the d-dimensional tropical climate model[J]. AIMS Mathematics, 2021, 6(6): 5581-5595. doi: 10.3934/math.2021330

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Abstract

This paper investigates the Cauchy problem on the d-dimensional tropical climate model with fractional hyperviscosity. We establish the small data global well-posedness of solutions to this model with supercritical dissipation. Furthermore, we study the asymptotic stability of these global solutions and obtain the optimal decay rates by using energy method and the method of bootstrapping argument.

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