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 $\|\theta(t)\|_{H^{2-2\alpha}}$ decays to zero as time goes to infinity. Fourier analysis and standard techniques are used.