Abstract : In this paper, we consider the Cauchy problem to the tropical climate model. We establish the global regularity for the 2D tropical climate model with generalized nonlocal dissipation of the barotropic mode and obtain a multi-logarithmical vorticity blow-up criterion for the 2D tropical climate model without any dissipation of the barotropic mode.
Keywords : Tropical climate model, global regularity, blow-up criterion
MSC numbers : Primary 35D35, 76D03
Supported by : The work is supported by Natural Science Foundation of Anhui Province (No.1908085 QA05)