Asymptotic study of supercritical surface Quasi-Geostrophic equation in critical space

Abstract

In this paper we prove, if $\theta \in C([0,\infty ),H^{2-2\alpha }({\mathbb{R}}^2))$ is a global solution of supercritical surface Quasi-Geostrophic equation with small initial data, then $\Vert \theta (t){\Vert }_{H^{2-2\alpha }}$ decays to zero as time goes to infinity. Fourier analysis and standard techniques are used.

global solution, supercritical surface Quasi-Geostrophic equation, Asymptotic study