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A new Bernstein's Inequality and the 2D Dissipative Quasi-Geostrophic Equation

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arxiv math/0607020 v3 pith:Z57JEPKG submitted 2006-07-01 math.AP

A new Bernstein's Inequality and the 2D Dissipative Quasi-Geostrophic Equation

Qionglei Chen , Changxing Miao , Zhifei Zhang This is my paper
classification math.AP
keywords inequalitybernsteincriticaldataequationinitialquasi-geostrophicwell-posedness
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We show a new Bernstein's inequality which generalizes the results of Cannone-Planchon, Danchin and Lemari\'{e}-Rieusset. As an application of this inequality, we prove the global well-posedness of the 2D quasi-geostrophic equation with the critical and super-critical dissipation for the small initial data in the critical Besov space, and local well-posedness for the large initial data.

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