Dong, Boqing; Chen, Zhi-Min Asymptotic stability of the critical and super-critical dissipative quasi-geostrophic equation. (English) Zbl 1109.76063 Nonlinearity 19, No. 12, 2919-2928 (2006). Summary: We examine the asymptotic stability for weak solution \(\theta\) of critical and supercritical dissipative quasi-geostrophic equation in Serrin-type class \(\nabla\theta\in L^r(0,\infty;L^p(R^2))\). This equation is perturbed by large initial data and external functions. It is shown that every weak perturbed solution \(\widetilde\theta\) has the same asymptotic behaviour as that of \(\theta\). More precisely, the difference \(\widetilde\theta(t)-\theta(t)\) decays in the norm of \(L^2(R^2)\). Cited in 1 ReviewCited in 22 Documents MSC: 76U05 General theory of rotating fluids 35Q35 PDEs in connection with fluid mechanics Keywords:weak solution PDFBibTeX XMLCite \textit{B. Dong} and \textit{Z.-M. Chen}, Nonlinearity 19, No. 12, 2919--2928 (2006; Zbl 1109.76063) Full Text: DOI