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Asymptotic profile of solutions to the two-dimensional dissipative quasi-geostrophic equation. (English) Zbl 1214.35049
Summary: This paper is concerned with the asymptotic behavior of the two-dimensional dissipative quasi-geostrophic equation. Based on the spectral decomposition of the Laplacian operator and iterative techniques, we obtain improved ${L}^{2}$ decay rates of weak solutions and derive more explicit upper bounds of higher order derivatives of solutions. We also prove the asymptotic stability of the subcritical quasi-geostrophic equation under large initial and external perturbations.
##### MSC:
 35Q35 PDEs in connection with fluid mechanics 76B03 Existence, uniqueness, and regularity theory (fluid mechanics) 35B40 Asymptotic behavior of solutions of PDE 35D30 Weak solutions of PDE 35B45 A priori estimates for solutions of PDE 86A05 Hydrology, hydrography, oceanography 35B30 Dependence of solutions of PDE on initial and boundary data, parameters
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