Global Well-Posedness and Energy Decay for Hypodissipative 3D Tropical Climate Models with damping

In this paper we consider a three-dimensional Tropical Climate Model with fractional diffusion Λ2α u 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. 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.