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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 $\overset \circ \to{B}^{1-\alpha}_{\infty,q}$, and global well-posedness of the critical quasi-geostrophic equation in ${\overset \circ \to{B}^{0}_{\infty,q}}$ for all $1 \leq q < \infty $. Here ${\overset \circ \to{B}^{s}_{\infty,q} }$ is the closure of the Schwartz functions in the norm of ${B^{s}_{\infty,q}}$.

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)
Full Text: DOI
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