Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016
qr-code QR
Code

Article

HOME ALL ARTICLES View

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.

The $H^1$-uniform attractor for the 2D non-autonomous tropical climate model on some unbounded domains

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

Abstract

Go to

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.

Article Tools

Stats or Metrics

Share this article on :

Related articles in BKMS

more +