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Global regularity of 2D tropical climate model with zero thermal diffusion
Author(s) -
Ye Zhuan
Publication year - 2020
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.201900132
Subject(s) - baroclinity , barotropic fluid , dissipation , mode (computer interface) , zero (linguistics) , diffusion , thermal , mathematics , supercritical fluid , climatology , mathematical analysis , physics , mechanics , meteorology , geology , computer science , thermodynamics , linguistics , philosophy , operating system
This article studies the global regularity problem of the two‐dimensional zero thermal diffusion tropical climate model with fractional dissipation, given by( − Δ ) α u in the barotropic mode equation and by( − Δ ) β v in the first baroclinic mode of the vector velocity equation. More precisely, we show that the global regularity result holds true as long as α + β ≥ 2 with 1 < α < 2 . In addition, with no dissipation from both the temperature and the first baroclinic mode of the vector velocity, we also establish the global regularity result with the dissipation strength at the logarithmically supercritical level. Finally, our arguments can be extended to obtain the corresponding global regularity results of the higher dimensional cases.