Global Well‐Posedness of the Three‐Dimensional Primitive Equations with Only Horizontal Viscosity and Diffusion |
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| Authors: | Chongsheng Cao Jinkai Li Edriss S. Titi |
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| Affiliation: | 1. Department of Mathematics, Florida International University, Miami, FL, USA;2. Department of Computer Science and Applied Mathematics, Weizmann Institute of Science, Rehovot, Israel;3. Department of Mathematics, Texas A&M University, TX, USA |
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| Abstract: | 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 Lq‐norms up to a logarithm of the Lp‐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.© 2016 Wiley Periodicals, Inc. |
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