On the 2D critical and supercritical dissipative quasi-geostrophic equation in Besov spaces |
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Authors: | Hongjie Dong Dong Li |
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Institution: | a Division of Applied Mathematics, Brown University, 182 George Street, Providence, RI 02912, USA b Department of Mathematics, University of Iowa, 14 MacLean Hall, Iowa City, IA 52242, USA |
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Abstract: | We prove the local smoothing effect of the 2D critical and supercritical dissipative quasi-geostrophic equations in critical Besov spaces. As an application, a global well-posedness result is established by adapting a method in Kiselev, Nazarov, and Volberg (2007) 16] and an idea in Dong and Du (2008) 15] with suitable modifications. Moreover, we show that the unique solution obtained in Chen, Miao, and Zhang (2007) 11] is a classical solution. These generalize some previous results in Dong (2010) 13], Dong and Du (2008) 15]. The main ingredients of the proofs are two commutator estimates and the preservation of suitable modulus of continuity of the solutions. |
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Keywords: | Higher regularity Critical and supercritical Quasi-geostrophic equations Global well-posedness |
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