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A maximum principle applied to quasi-geostrophic equations. (English) Zbl 1309.76026
Summary: We study the initial value problem for dissipative 2D quasi-geostrophic equations proving local existence, global results for small initial data in the super-critical case, decay of \(L^p\) -norms and asymptotic behavior of viscosity solution in the critical case. Our proofs are based on a maximum principle valid for more general flows.

MSC:
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
35Q35 PDEs in connection with fluid mechanics
76U05 General theory of rotating fluids
86A05 Hydrology, hydrography, oceanography
26A33 Fractional derivatives and integrals
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