Open AccessOn long-time asymptotic behavior for solutions to 2D temperature-dependent tropical climate model
Author(s) -
Chaoying Li,
Xiaojing Xu,
Zhuan Ye
Publication year - 2022
Publication title -
discrete and continuous dynamical systems
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.289
H-Index - 70
eISSN - 1553-5231
pISSN - 1078-0947
DOI - 10.3934/dcds.2021163
Subject(s) - sobolev space , order (exchange) , mathematics , combinatorics , space (punctuation) , integer (computer science) , pure mathematics , computer science , finance , economics , programming language , operating system
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 \begin{document}$ k $\end{document} -order of the solution actually decays at least at the rate of \begin{document}$ (1+t)^{-\frac{k}{2}} $\end{document} .