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Asymptotic stability of the critical and super-critical dissipative quasi-geostrophic equation. (English) Zbl 1109.76063

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 \(L^2(R^2)\).

MSC:

76U05 General theory of rotating fluids
35Q35 PDEs in connection with fluid mechanics

Keywords:

weak solution
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