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

doi:10.1016/S0252-9602(17)30061-9

数学物理学报(英文版) ›› 2017, Vol. 37 ›› Issue (4): 1115-1132.doi: 10.1016/S0252-9602(17)30061-9

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

程峰¹, 李维喜², 徐超江¹

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

收稿日期:2015-12-28 修回日期:2017-01-05 出版日期:2017-08-25 发布日期:2017-08-25
作者简介:Feng CHENG,E-mail:chengfengwhu@whu.edu.cn;Wei-Xi LI,E-mail:wei-xi.li@whu.edu.cn;Chao-Jiang XU,E-mail:chjxu.math@whu.edu.cn
基金资助:
The second author is supported by NSF of China (11422106) and Fok Ying Tung Education Foundation (151001) and the third author is supported by "Fundamental Research Funds for the Central Universities" and the NSF of China (11171261).

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

Feng CHENG¹, Wei-Xi LI², Chao-Jiang XU¹

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

Received:2015-12-28 Revised:2017-01-05 Online:2017-08-25 Published:2017-08-25
About author:Feng CHENG,E-mail:chengfengwhu@whu.edu.cn;Wei-Xi LI,E-mail:wei-xi.li@whu.edu.cn;Chao-Jiang XU,E-mail:chjxu.math@whu.edu.cn
Supported by:
The second author is supported by NSF of China (11422106) and Fok Ying Tung Education Foundation (151001) and the third author is supported by "Fundamental Research Funds for the Central Universities" and the NSF of China (11171261).

摘要/Abstract

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 L²-estimate, and the main difficulty arises from the estimate on the pressure term due to the appearance of weight function.

关键词: Gevrey class regularity, incompressible Euler equation, weighted Sobolev space

Abstract:

Key words: Gevrey class regularity, incompressible Euler equation, weighted Sobolev space

程峰, 李维喜, 徐超江. GEVREY REGULARITY WITH WEIGHT FOR INCOMPRESSIBLE EULER EQUATION IN THE HALF PLANE[J]. 数学物理学报(英文版), 2017, 37(4): 1115-1132.

Feng CHENG, Wei-Xi LI, Chao-Jiang XU. GEVREY REGULARITY WITH WEIGHT FOR INCOMPRESSIBLE EULER EQUATION IN THE HALF PLANE[J]. Acta mathematica scientia,Series B, 2017, 37(4): 1115-1132.

参考文献

[1] Chemin J Y, Desjardins B, Gallagher I, et al. Mathematical Geophysics. An Introduction to Rotating Fluids and the Navier-Stokes Equations. Oxford Lecture Series in Mathematics and its Applications, 32. Oxford:The Clarendon Press, Oxford University Press, 2006
[2] Bourguignon J P, Brezis H. Remarks on the Euler equation. J Funct Anal, 1974, 15:341-363
[3] Chen Hua, Li Weixi, Xu Chaojiang. Gevrey regularity of subelliptic Monge-Ampére equations in the plane. Adv Math, 2011, 228(3):1816-1841
[4] Chen Hua, Li Weixi, Xu Chaojiang. Gevrey hypoellipticity for a class of kinetic equations. Comm Partial Differ Equ, 2011, 36(4):693-728
[5] Chen Hua, Li Weixi, Xu Chaojiang. Analytic smoothness effect of solutions for spatially homogeneous Landau equation. J Differ Equ, 2010, 248(1):77-94
[6] Chen Hua, Li Weixi, Xu Chaojiang. Gevrey hypoellipticity for linear and non-linear Fokker-Planck equations. J Differ Equ, 2009, 246(1):320-339
[7] Ebin D G, Marsden J E. Groups of diffeomorphisms and the solution of the classical Euler equations for a perfect fluid. Bull Amer Math Soc, 1969, 75:962-967
[8] Kukavica I, Vicol V C. The domain of analyticity of solutions to the three-dimensional Euler equations in a half space. Discrete Contin Dyn Syst, 2011, 29(1):285-303
[9] Kukavica I, Vicol V. On the analyticity and Gevrey-class regularity up to the boundary for the Euler equations. Nonlinearity, 2011, 24(3):765-796
[10] Kato T. Nonstationary flows of viscous and ideal fluids in R³. J Funct Anal, 1972, 9:296-305
[11] Kato T. On classical solutions of the two-dimensional nonstationary Euler equation. Arch Rational Mech Anal, 1967, 25:188-200
[12] Taylor M E. Partial Differential Equations. Ⅲ. Nonlinear Equations. Corrected reprint of the 1996 original. New York:Springer-Verlag, 1997
[13] Temam R. On the Euler equations of incompressible perfect fluids. J Funct Anal, 1975, 20(1):32-43
[14] Fioas C, Frisch U, Temam R. Existence de solutions C^∞ des équations d'Euler. (French) C R Acad Sci Paris Sér A-B, 1975, 280:A505-A508
[15] Yudovich V I. Non-stationary flows of an ideal incompressible fluid. Zh Vychisl Mat Mat Fiz, 1963, 3(6):1032-1066
[16] Oliver M. Classical solutions a generalized Euler equation in two dimensions. J Math Anal Appl, 1997, 215(2):471-484
[17] Chen H, Li W X, Xu C J. Gevrey regularity for solution of the spatially homogeneous Landou equation. Acta Math Sci, 2009, 29B(3):673-686

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

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

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