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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:
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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