Almost Global Existence for the Prandtl Boundary Layer Equations

被引：80
作者：
Ignatova, Mihaela [1 ]
Vicol, Vlad [1 ]
机构：
[1] Princeton Univ, Dept Math, Princeton, NJ 08544 USA
来源：
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2016年 / 220卷 / 02期
基金：
美国国家科学基金会;
关键词：
HYDROSTATIC EULER EQUATIONS; ANALYTIC SOLUTIONS; LOCAL EXISTENCE; WELL-POSEDNESS; ILL-POSEDNESS; HALF-SPACE; DOMAIN; UNIQUENESS; LIMIT;
D O I：
10.1007/s00205-015-0942-2
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the Prandtl boundary layer equations on the half plane, with initial datum that lies in a weighted H-1 space with respect to the normal variable, and is real-analytic with respect to the tangential variable. The boundary trace of the horizontal Euler flow is taken to be a constant. We prove that if the Prandtl datum lies within epsilon of a stable profile, then the unique solution of the Cauchy problem can be extended at least up to time T-epsilon >= exp(epsilon(-1)/log(epsilon(-1))).
引用
收藏
页码：809 / 848
页数：40
相关论文
共 42 条
[11]   Remarks on the ill-posedness of the Prandtl equation [J].
Gerard-Varet, D. ;
Nguyen, T. .
ASYMPTOTIC ANALYSIS, 2012, 77 (1-2) :71-88
[12]  
Gerard-Varet D., 2013, ARXIV13050221
[13]  
Gérard-Varet D, 2010, J AM MATH SOC, V23, P591
[14]  
Grenier E, 2000, J DIFFER EQUATIONS, V164, P180, DOI 10.1006/jdeq.1993.3713
[15]  
Grenier E, 2000, COMMUN PUR APPL MATH, V53, P1067
[16]  
Grenier E., 2014, ARXIV14063862
[17]  
Grenier E., 2014, ARXIV14064452
[18]  
Grenier E., 2014, ARXIV14021395
[19]   A Note on Prandtl Boundary Layers [J].
Guo, Yan ;
Toan Nguyen .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2011, 64 (10) :1416-1438
[20]  
Hong L., 2003, Commun. Math. Sci., V1, P293, DOI 10.4310/CMS.2003.v1.n2.a5
12345