Existence of Solutions for Three Dimensional Stationary Incompressible Euler Equations with Nonvanishing Vorticity

被引：13
作者：
Tang, Chunlei [1 ,2 ]
Xin, Zhouping [2 ]
机构：
[1] Southwest Univ, Dept Math, Chongqing 400715, Peoples R China
[2] Chinese Univ Hong Kong, Inst Math Sci, Hong Kong, Hong Kong, Peoples R China
来源：
CHINESE ANNALS OF MATHEMATICS SERIES B | 2009年 / 30卷 / 06期
基金：
中国国家自然科学基金;
关键词：
Three dimensional stationary incompressible Euler equations; Boundary value condition; Nonvanishing vorticity; PSEUDO-ADVECTION METHOD; STATISTICAL-MECHANICS DESCRIPTION; SYMMETRIC VORTEX PAIRS; DIMENSIONS; IDEAL FLUID; STEADY; RINGS; FLOW; SWIRL;
D O I：
10.1007/s11401-009-0092-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, solutions with nonvanishing vorticity are established for the three dimensional stationary incompressible Euler equations on simply connected bounded three dimensional domains with smooth boundary. A class of additional boundary conditions for the vorticities are identified so that the solution is unique and stable.
引用
收藏
页码：803 / 830
页数：28
相关论文
共 39 条
[1]   EXISTENCE OF 3-DIMENSIONAL, STEADY, INVISCID, INCOMPRESSIBLE FLOWS WITH NONVANISHING VORTICITY [J].
ALBER, HD .
MATHEMATISCHE ANNALEN, 1992, 292 (03) :493-528
[2]   EXISTENCE OF STEADY VORTEX RINGS IN AN IDEAL FLUID [J].
AMBROSETTI, A ;
STRUWE, M .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1989, 108 (02) :97-109
[3]   Existence of steady symmetric vortex pairs on a planar domain with an obstacle [J].
Badiani, TV .
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1998, 123 :365-384
[4]   On the existence of non-linear force-free fields in three-dimensional domains [J].
Boulmezaoud, TZ ;
Amari, T .
ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2000, 51 (06) :942-967
[5]   STEADY SYMMETRIC VORTEX PAIRS AND REARRANGEMENTS [J].
BURTON, GR .
PROCEEDINGS OF THE ROYAL SOCIETY OF EDINBURGH SECTION A-MATHEMATICS, 1988, 108 :269-290
[6]   A SPECIAL-CLASS OF STATIONARY FLOWS FOR 2-DIMENSIONAL EULER EQUATIONS - A STATISTICAL-MECHANICS DESCRIPTION .2. [J].
CAGLIOTI, E ;
LIONS, PL ;
MARCHIORO, C ;
PULVIRENTI, M .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1995, 174 (02) :229-260
[7]   A SPECIAL-CLASS OF STATIONARY FLOWS FOR 2-DIMENSIONAL EULER EQUATIONS - A STATISTICAL-MECHANICS DESCRIPTION [J].
CAGLIOTI, E ;
LIONS, PL ;
MARCHIORO, C ;
PULVIRENTI, M .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1992, 143 (03) :501-525
[8]  
CHACON T, 1987, LECT NOTES CONTR INF, V97, P175, DOI 10.1007/BFb0038751
[9]  
CHACON T, 1986, LECT NOTES CONTR INF, V84, P170
[10]   THE TOPOLOGY OF STATIONARY CURL PARALLEL SOLUTIONS OF EULER EQUATIONS [J].
CHICONE, C .
ISRAEL JOURNAL OF MATHEMATICS, 1981, 39 (1-2) :161-166
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