Global in Time Classical Solutions to the 3D Quasi-Geostrophic System for Large Initial Data
Global in Time Classical Solutions to the 3D Quasi-Geostrophic System for Large Initial Data
复制标题
大型初始数据 3D 准地转系统的全球及时经典解
DOI：
10.1007/s00220-017-3049-9
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发表时间：
2016
影响因子：
2.4
通讯作者：
A. Vasseur
中科院分区：
文献类型：
--
作者：
Matthew Novack;A. Vasseur
本文证明了具有Ekman泵浦的三维准地转系统对于任意光滑初始值（可能很大）的全局时间经典解的存在性。该系统将$${\mathbb{R}^3_+}$$ R+3中的无粘输运方程与迹线所满足的边界方程耦合在一起。该证明结合了边界$${z=0}$$ z=0上的De Giorgi正则化效应（类似于所谓的表面准地转方程）和Beale-Kato-Majda技术来传播$${z > 0}$$ z>的正则性。结合势理论和Littlewood-Paley技术的自适应论证，增强了Besov空间B ＿∞，∞1处迹线的正则化效果。
In this paper, the authors show the existence of global in time classical solutions to the 3D quasi-geostrophic system with Ekman pumping for any smooth initial value (possibly large). This system couples an inviscid transport equation in $${\mathbb{R}^3_+}$$R+3 with an equation on the boundary satisfied by the trace. The proof combines the De Giorgi regularization effect on the boundary $${z=0}$$z=0—similar to the so called surface quasi-geostrophic equation—with Beale–Kato–Majda techniques to propagate regularity for $${z > 0}$$z>0. A bootstrapping argument combining potential theory and Littlewood–Paley techniques is used to strengthen the regularization effect on the trace up to the Besov space B̊∞,∞1.