Global regularity results for the climate model with fractional dissipation

This paper studies the global well-posedness problem on a tropical climate model with fractional dissipation. This system allows us to simultaneously examine a family of equations characterized by the fractional dissipative terms $ (-Δ)^{\mathit{\alpha }}u$ in the equation of the barotropic mode $ u$ and $ (-Δ)^β v$ in the equation of the first baroclinic mode $ v$. We establish the global existence and regularity of the solutions when the total fractional power is 2, namely $ {\mathit{\alpha }}+ β = 2$.