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Global strong solutions and time decay of 2D tropical climate model with zero thermal diffusion
Author(s) -
Zhai Xiaoping,
Chen Yiren
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6452
Subject(s) - barotropic fluid , dissipative system , baroclinity , mathematics , diffusion , mode (computer interface) , heat equation , zero (linguistics) , mathematical analysis , climatology , physics , thermodynamics , geology , linguistics , philosophy , computer science , operating system
The global small solutions of the tropical climate model are obtained with the fractional dissipative terms Λ α u in the equation of the barotropic mode u and Λ α v in the equation of the first baroclinic mode v . More precisely, we prove for 1< α ≤ 2 that the couple system has global unique strong solutions for small initial data with critical regularities. Moreover, the smallness assumption imposed on the initial barotropic mode of the velocity can be removed if α =2. We also study the large time behavior of the constructed solutions and obtain optimal time decay rates by a pure energy argument.