Global smooth solution of 2D temperature-dependent tropical climate model

Nonlinearity ◽  
2021 ◽  
Vol 34 (8) ◽  
pp. 5662-5686
Author(s):  
Bo-Qing Dong ◽  
Chaoying Li ◽  
Xiaojing Xu ◽  
Zhuan Ye
Keyword(s):  
Smooth Solution ◽  
Climate Model ◽  
Tropical Climate ◽  
Temperature Dependent ◽  
Global Smooth Solution ◽  
Tropical Climate Model

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

2021 ◽  
Vol 0 (0) ◽  
pp. 0
Author(s):  
Chaoying Li ◽  
Xiaojing Xu ◽  
Zhuan Ye
Keyword(s):  
Asymptotic Behavior ◽  
Initial Data ◽  
Climate Model ◽  
Tropical Climate ◽  
Two Dimensional ◽  
Temperature Dependent ◽  
General Initial Data ◽  
Long Time ◽  
Tropical Climate Model ◽  
Time Asymptotic Behavior

<p style='text-indent:20px;'>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 <inline-formula><tex-math id="M1">\begin{document}$ k $\end{document}</tex-math></inline-formula>-order of the solution actually decays at least at the rate of <inline-formula><tex-math id="M2">\begin{document}$ (1+t)^{-\frac{k}{2}} $\end{document}</tex-math></inline-formula>.</p>

scholarly journals Energy Conservation for 3D Tropical Climate Model in Periodic Domains

2021 ◽  
Vol 2021 ◽  
pp. 1-4
Author(s):  
Hui Zhang
Keyword(s):  
Energy Conservation ◽  
Euler Equations ◽  
Weak Solutions ◽  
Climate Model ◽  
Sufficient Conditions ◽  
Tropical Climate ◽  
Tropical Climate Model ◽  
Periodic Domains ◽  
Onsager’S Conjecture

In this paper, we prove the energy conservation for the weak solutions of the 3D tropical climate model under some sufficient conditions. Our results are similar to Onsager’s conjecture which is on energy conservation for weak solutions of Euler equations.

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