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Tropical climate model derived by Frierson et al. (Commun Math Sci 2:591–626, 2004) and its modified versions have been investigated in a number of papers [see, e.g., Li and Titi (Discrete Contin Dyn Syst Series A 36(8):4495–4516, 2016), Wan (J Math Phys 57(2):021507, 2016), Ye (J Math Anal Appl 446:307–321, 2017) and more recently Dong et al. (Discrete Contin Dyn Syst Ser B 24(1):211–229, 2019)]. Here, we deal with the 2 D  tropical climate model with fractional dissipative terms in the equation of the barotropic mode  u  and in the equation of the first baroclinic mode  v  of the velocity, but without diffusion in the temperature equation, and we establish a regularity criterion for this system.

A regularity criterion for a 2D tropical climate model with fractional dissipation