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Global solutions of the super-critical 2D quasi-geostrophic equation in Besov spaces. (English) Zbl 1119.76070
Summary: We study the super-critical 2D dissipative quasi-geostrophic equation. We obtain some regularization effects allowing us to prove a global well-posedness result for small initial data lying in critical Besov spaces constructed over Lebesgue spaces \(L^{p}\), with \(p \in [1,\infty]\). Local results for arbitrary initial data are also given.

MSC:
76U05 General theory of rotating fluids
35Q35 PDEs in connection with fluid mechanics
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