Uniform pointwise asymptotics of solutions to quasi-geostrophic equation

Abstract

We provide two-sided pointwise estimates and uniform asymptotics of the solutions to the subcritical quasi-geostrophic equation with initial data in $L^{2/(\alpha -1)}({\mathbb{R}}^2)$. Furthermore, we give upper bound of similar type for any derivative of the solutions. Initial data in $L^p({\mathbb{R}}^2)$, $p>2/(\alpha -1)$, are also discussed.