Global regularity of 2D Rayleigh-B\'{e}nard equations with logarithmic supercritical dissipation

Abstract

In this paper, we study the global regularity problem for the 2D Rayleigh-B\'{e}nard equations with logarithmic supercritical dissipation. By exploiting a combined quantity of the system, the technique of Littlewood-Paley decomposition and Besov spaces, and some commutator estimates, we establish the global regularity of a strong solution to this equations in the Sobolev space $H^{s}(\mathbb{R}^{2})$ for $s \ge2$.