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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:
35Q35PDEs in connection with fluid mechanics
76B03Existence, uniqueness, and regularity theory (fluid mechanics)
35B40Asymptotic behavior of solutions of PDE
35D30Weak solutions of PDE
35B45A priori estimates for solutions of PDE
86A05Hydrology, hydrography, oceanography
35B30Dependence of solutions of PDE on initial and boundary data, parameters
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