Global regularity for a class of 2D tropical climate model

In this paper, we establish the global regularity of a modified version of the tropical climate model originally derived by Frierson–Majda–Pauluis (2004) [6] which couples the barotropic and baroclinic modes of the velocity and the typical midtropospheric temperature. In proving the global regularity, to bypass the difficulty caused by the very weak dissipation (any small power α>0α>0) of the barotropic mode, we utilize the “weakly nonlinear” energy estimate approach and the Maximal LtqLxp regularity for the heat kernel.