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

Tropical climate model derived by Frierson-Majda-Pauluis (2004) and its modified versions have been investigated in a number of papers (see, e.g., Li and Titi (2016), Wan (2016), Ye (2017) and more recently Zhu (2018) and Dong-Wang-Wu-Zhang (2019)). Here, we deal with the 2D viscous tropical climate model with fractional dissipation 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.