Global well-posedness and energy decay for hypodissipative three-dimensional tropical climate models with damping

Abstract In this paper, we consider a three-dimensional tropical climate model (TCM) with fractional diffusion Λ2αu and, in particular, nonlinear damping |u|β−1u in the equation for the barotropic mode of the velocity u. Assuming α∈(9/10,1] and exploiting the regularizing effect due to the damping term, we establish the global existence and uniqueness of strong solutions for β greater than a suitable threshold depending on α. In the given analysis, we place particular emphasis on the case of hypoviscosity. As a further result, we prove the L2-energy decay of the global solution (u,v,θ) over the long-time period.