Low regularity global well-posedness for 2D Boussinesq equations with variable viscosity

Abstract

As a continuation of our previous work, we consider lower regularity global well-posedness for a model of the two-dimensional zero diffusivity Boussinesq equations with variable viscosity. More precisely, based on De Giorgi–Nash–Moser estimates and the refined logarithmic Gronwall-type inequality, we prove that it is globally well-posed, provided that the initial data belong to Hswith s > 1. Finally, we show that it is also valid for the two-dimensional zero diffusivity Boussinesq equations with variable viscosity in the non-divergence form.