Global small solutions to a tropical climate model without thermal diffusion
Global small solutions to a tropical climate model without thermal diffusion
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DOI：
10.1063/1.4941039
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发表时间：
2015-06
影响因子：
1.3
通讯作者：
Renhui Wan
中科院分区：
文献类型：
--
作者：
Renhui Wan
在小的初始数据下，我们得到了一个热带气候模式经典解的整体适定性，该模式只考虑了第一斜压模式的速度（−ηΔv）耗散.该模型是由Frierson-Majda-Pauluis在Frierson等人[Commun.数学科学2，591-626（2004）]。主要的困难是没有热扩散。为了克服这个问题，我们利用了来自耦合项，耗散项和阻尼项的方程的结构。然后，我们发现隐藏的热扩散。此外，基于Littlewood-Paley理论，我们建立了一个广义交换子估计，该估计可应用于其他偏微分方程。
We obtain the global well-posedness of classical solutions to a tropical climate model with only the dissipation of the first baroclinic model of the velocity (−ηΔv) under small initial data. This model is a modified version of the original system derived by Frierson-Majda-Pauluis in Frierson et al. [Commun. Math. Sci. 2, 591-626 (2004)]. The main difficulty is the absence of thermal diffusion. To overcome it, we exploit the structure of the equations coming from the coupled terms, dissipation term, and damp term. Then, we find the hidden thermal diffusion. In addition, based on the Littlewood-Paley theory, we establish a generalized commutator estimate, which may be applied to other partial differential equations.