scholarly journals Long-time asymptotic behavior of two-dimensional dissipative Boussinesq systems

2009 ◽  
Vol 2 (1) ◽  
pp. 37-53 ◽  
Author(s):  
Min Chen ◽  
◽  
Olivier Goubet ◽  
Keyword(s):  
Asymptotic Behavior ◽  
Two Dimensional ◽  
Long Time ◽  
Boussinesq Systems ◽  
Time Asymptotic Behavior

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 Long Time Behavior of the Solution of the Two-Dimensional Dissipative QGE in Lei–Lin Spaces

2020 ◽  
Vol 2020 ◽  
pp. 1-6
Author(s):  
Moez Benhamed ◽  
Sahar Mohammad Abusalim
Keyword(s):  
Asymptotic Behavior ◽  
Time Behavior ◽  
Two Dimensional ◽  
Long Time Behavior ◽  
Long Time

In this paper, we study the asymptotic behavior of the two-dimensional quasi-geostrophic equations with subcritical dissipation. More precisely, we establish that θtX1−2α vanishes at infinity.

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