A Frequency Localized Maximum Principle Applied to the 2D Quasi-Geostrophic Equation |
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| Authors: | Henggeng Wang Zhifei Zhang |
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| Affiliation: | 1.School of Mathematics and Statistics,Zhejiang University of Finance and Economics,Hangzhou,P. R. China;2.School of Mathematical Science,Peking University,Beijing,P. R. China |
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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 mathringB1-a￥,q{mathring{B}^{1-alpha}_{infty,q}}, and global well-posedness of the critical quasi-geostrophic equation in mathringB0￥,q{mathring{B}^{0}_{infty,q}} for all 1 ≤ q < ∞. Here mathringBs￥,q {mathring{B}^{s}_{infty,q} } is the closure of the Schwartz functions in the norm of Bs￥,q{B^{s}_{infty,q}}. |
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