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

Qionglei Chen·Changxing Miao·Zhifei Zhang
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Abstract

We show a new Bernstein's inequality which generalizes the results of Cannone-Planchon, Danchin and Lemarié-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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Qionglei Chen, Changxing Miao, Zhifei Zhang. 2007-01-25. A new Bernstein's Inequality and the 2D Dissipative Quasi-Geostrophic Equation. https://doi.org/10.1007/s00220-007-0193-7

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