Global Well-Posedness of the Three-Dimensional Primitive Equations with Only Horizontal Viscosity and Diffusion

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• 作者：Chongsheng Cao ; Jinkai Li and Edriss S. Titi
• 刊名：Communications on Pure and Applied Mathematics
• 出版年：2016
• 出版时间：August 2016
• 年：2016
• 卷：69
• 期：8
• 页码：1492-1531
• 全文大小：325K
• ISSN：1097-0312

文摘

In this paper, we consider the initial boundary value problem of the three-dimensional primitive equations for planetary oceanic and atmospheric dynamics with only horizontal eddy viscosity in the horizontal momentum equations and only horizontal diffusion in the temperature equation. Global well-posedness of the strong solution is established for any H² initial data. An N-dimensional logarithmic Sobolev embedding inequality, which bounds the L^∞-norm in terms of the L^q-norms up to a logarithm of the L^p-norm for p > N of the first-order derivatives, and a system version of the classic Grönwall inequality are exploited to establish the required a~priori H² estimates for global regularity.