Stability Analysis of the Supercritical Surface Quasi-Geostrophic Equation

Abstract

This paper is devoted to the study of the stability issue of the supercritical dissipative surface quasi-geostrophic equation with nondecay low-regular external force. Supposing that the weak solution $\theta (x,t)$ of the surface quasi-geostrophic equation with the force $f\in L^2(0,T;H^{-\alpha /2}{(\mathrm{ℝ}}^2))$ satisfies the growth condition in the critical BMO space $\nabla \theta \in L^1(0,\mathrm{\infty };\text{BMO})$, it is proved that every perturbed weak solution $\bar{\theta }(t)$ converges asymptotically to solution $\theta (t)$ of the original surface quasi-geostrophic equation. The initial and external forcing perturbations are allowed to be large.