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A Frequency Localized Maximum Principle Applied to the 2D Quasi-Geostrophic Equation

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Abstract

In this paper, we prove a maximum principle for a frequency localized transport-diffusion equation. As an application, we prove the local well-posedness of the supercritical quasi-geostrophic equation in the critical Besov spaces \({\mathring{B}^{1-\alpha}_{\infty,q}}\), and global well-posedness of the critical quasi-geostrophic equation in \({\mathring{B}^{0}_{\infty,q}}\) for all 1 ≤ q < ∞. Here \({\mathring{B}^{s}_{\infty,q} }\) is the closure of the Schwartz functions in the norm of \({B^{s}_{\infty,q}}\).

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Authors and Affiliations

  1. School of Mathematics and Statistics, Zhejiang University of Finance and Economics, Hangzhou, 310018, P. R. China

    Henggeng Wang

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

    Zhifei Zhang

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  1. Henggeng Wang
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  2. Zhifei Zhang
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Correspondence to Zhifei Zhang.

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Communicated by P. Constantin

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Wang, H., Zhang, Z. A Frequency Localized Maximum Principle Applied to the 2D Quasi-Geostrophic Equation. Commun. Math. Phys. 301, 105–129 (2011). https://doi.org/10.1007/s00220-010-1144-2

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  • DOI: https://doi.org/10.1007/s00220-010-1144-2

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