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A new Bernstein’s inequality and the 2D dissipative quasi-geostrophic equation. (English) Zbl 1142.35069
A new Bernstein’s inequality is proven and applied to the prove of global well-posedness of the two-dimensional quasi-geostrophic equation for small initial data in the critical Besov space. Local well-posedness can be shown in case of large initial data.

MSC:
35Q35PDEs in connection with fluid mechanics
76D03Existence, uniqueness, and regularity theory
86A05Hydrology, hydrography, oceanography
35B30Dependence of solutions of PDE on initial and boundary data, parameters
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