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A frequency localized maximum principle applied to the 2D quasi-geostrophic equation. (English) Zbl 1248.35211
Summary: In this paper, we prove a maximum principle for a frequency localized transport-diffusion equation. As an application, we prove the local well-posedness of the supercritical quasi-geostrophic equation in the critical Besov spaces B ,q 1-α , and global well-posedness of the critical quasi-geostrophic equation in B ,q 0 for all 1q<. Here B ,q s is the closure of the Schwartz functions in the norm of B ,q s .
MSC:
35Q86PDEs in connection with geophysics
35Q35PDEs in connection with fluid mechanics
35B30Dependence of solutions of PDE on initial and boundary data, parameters
76B03Existence, uniqueness, and regularity theory (fluid mechanics)
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