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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.

35Q35 PDEs in connection with fluid mechanics
76D03 Existence, uniqueness, and regularity theory for incompressible viscous fluids
86A05 Hydrology, hydrography, oceanography
35B30 Dependence of solutions to PDEs on initial and/or boundary data and/or on parameters of PDEs
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