The 2D Boussinesq-Navier-Stokes Equations with Logarithmically Supercritical Dissipation

Abstract

This paper studies 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 symbol of L is represented by |ξ| a(|ξ|) with a satisfying lim|ξ|→∞ a(|ξ|) |ξ|σ = 0 for any σ > 0, we obtain the global well-posedness. A special consequence is the global well-posedness when the dissipation is logarithmically supercritical.