(untitled) (Journal of Mathematical Study, 2024)
We study the global well-posedness of the initial-value problem for the 2D Boussinesq-Navier-Stokes equations with dissipation given by an operator L that can be defined through both an integral kernel and a Fourier multiplier. When the operator L is represented by |ξ|a(|ξ|) with a satisfying _|ξ|→ ∞ a(|ξ|)|ξ|^σ = 0 for any σ>0, we obtain the global well-posedness. A special consequence is the global well-posedness of 2D Boussinesq-Navier-Stokes equations when the dissipation is logarithmically supercritical.