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A New Bernstein’s Inequality and the 2D Dissipative Quasi-Geostrophic Equation

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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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Authors and Affiliations

  1. Institute of Applied Physics and Computational Mathematics, P.O. Box 8009, Beijing, 100088, P. R. China

    Qionglei Chen & Changxing Miao

  2. School of Mathematical Science, Peking University, Beijing, 100871, P. R. China

    Zhifei Zhang

Authors
  1. Qionglei Chen
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  2. Changxing Miao
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  3. Zhifei Zhang
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Correspondence to Changxing Miao.

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Communicated by P. Constantin

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Chen, Q., Miao, C. & Zhang, Z. A New Bernstein’s Inequality and the 2D Dissipative Quasi-Geostrophic Equation. Commun. Math. Phys. 271, 821–838 (2007). https://doi.org/10.1007/s00220-007-0193-7

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  • DOI: https://doi.org/10.1007/s00220-007-0193-7

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