Asymptotic convergence rate of supercritical surface quasi-geostrophic equation in Morrey space

In this paper the asymptotic convergence rate of the supercritical surface quasi-geostrophic equation in Morrey space is investigated. It is shown that if the global solution θ(x,t)θ(x,t) of the supercritical surface quasi-geostrophic equation satisfies the growth condition in critical Morrey space∫0∞‖∇θ(t)‖M˙p,q(R2)rdt<∞for αr+2p=α,2α