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

35Q86 PDEs in connection with geophysics
35Q35 PDEs in connection with fluid mechanics
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
76B03 Existence, uniqueness, and regularity theory for incompressible inviscid fluids
Full Text: DOI
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