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GEVREY REGULARITY WITH WEIGHT FOR INCOMPRESSIBLE EULER EQUATION IN THE HALF PLANE 预览

GEVREY REGULARITY WITH WEIGHT FOR INCOMPRESSIBLE EULER EQUATION IN THE HALF PLANE
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摘要 In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical boundary layer equation for fast rotating fluid. The method presented here is based on the basic weighted L~2-estimate, and the main difficulty arises from the estimate on the pressure term due to the appearance of weight function. In this work we prove the weighted Gevrey regularity of solutions to the incompressible Euler equation with initial data decaying polynomially at infinity. This is motivated by the well-posedness problem of vertical boundary layer equation for fast rotating fluid. The method presented here is based on the basic weighted L^2-estimate, and the main difficulty arises from the estimate on the pressure term due to the appearance of weight function.
作者 程峰 李维喜 徐超江 Feng CHENG,Wei-Xi LI,Chao-diang XU(1.School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;2.School of Mathematics and Statistics, and Computational Science Hubei Key Laboratory, Wuhan University, Wuhan 430072, China)
出处 《数学物理学报:B辑英文版》 SCIE CSCD 2017年第4期1115-1132,共18页 Acta Mathematica Scientia
基金 The second author is supported by NSF of China (11422106) and Fok Ying Tung Education Foundation (151001) and the third author is supported by "Funda- mental Research Funds for the Central Universities" and the NSF of China (11171261).
关键词 可压缩EULER方程 正则性 半平面 重量 边界层方程 定性问题 旋转流体 权重函数 Gevrey class regularity incompressible Euler equation weighted Sobolev space
作者简介 E-mail:chengfengwhu@whu.edu.cn E-mail: chjxu.math@whu.edu.cn E-mail: chjxu.math@whu.edu.cn
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