Bull. Korean Math. Soc. 2022; 59(6): 1439-1470
Online first article August 31, 2022 Printed November 30, 2022
https://doi.org/10.4134/BKMS.b210800
Copyright © The Korean Mathematical Society.
Pigong Han, Keke Lei, Chenggang Liu, Xuewen Wang
University of Chinese Academy of Sciences; University of Chinese Academy of Sciences; Zhongnan University of Economics and Law; University of Chinese Academy of Sciences
In this paper, we study the uniform attractor of the 2D non-autonomous tropical climate model in an arbitrary unbounded domain on which the Poincar\'e inequality holds. We prove that the uniform attractor is compact not only in the $L^2$-spaces but also in the $H^1$-spaces. Our proof is based on the concept of asymptotical compactness. Finally, for the quasiperiodical external force case, the dimension estimates of such a uniform attractor are also obtained.
Keywords: Tropical climate model, asymptotical compactness, uniform attractor
MSC numbers: 35Q35, 35B40, 76D07
Supported by: This work is supported by the National Key R\&D Program of China (2021YFA1000800), the National Natural Science Foundation of China under Grant No. 11871457, the K. C. Wong Education Foundation, Chinese Academy of Sciences.
2020; 57(4): 891-907
2014; 51(5): 1299-1324
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