Exact periodic traveling water waves with vorticity

被引：42
作者：
Constantin, A
Strauss, W
机构：
[1] Lund Univ, Dept Math, S-22100 Lund, Sweden
[2] Brown Univ, Dept Math, Providence, RI 02912 USA
[3] Brown Univ, Lefschetz Ctr Dynam Syst, Providence, RI 02912 USA
来源：
COMPTES RENDUS MATHEMATIQUE | 2002年 / 335卷 / 10期
关键词：
D O I：
10.1016/S1631-073X(02)02565-7
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
For the classical inviscid water wave problem under the influence of gravity, described by the Euler equation with a free surface over a flat bottom, we construct periodic traveling waves with vorticity. They are symmetric waves whose profiles are monotone between each crest and trough. We use global bifurcation theory to construct a connected set of such solutions. This set contains flat waves as well as waves that approach flows with stagnation points.
引用
收藏
页码：797 / 800
页数：4
相关论文
共 24 条
[1]   ON THE STOKES CONJECTURE FOR THE WAVE OF EXTREME FORM [J].
AMICK, CJ ;
FRAENKEL, LE ;
TOLAND, JF .
ACTA MATHEMATICA, 1982, 148 :193-214
[2]   The rotational flow of finite amplitude periodic water waves on shear currents [J].
Baddour, RE ;
Song, SW .
APPLIED OCEAN RESEARCH, 1998, 20 (03) :163-171
[3]   On the deep water wave motion [J].
Constantin, A .
JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL, 2001, 34 (07) :1405-1417
[4]  
CONSTANTIN A, 2002, UNPUB EXACT STEADY P
[5]  
Crandal M.G., 1971, J. Funct. Anal, V8, P321, DOI 10.1016/0022-1236(71)90015-2
[6]  
DUBREILJACOTIN ML, 1937, J MATH PURE APPL, V13, P217
[7]  
Gerstner F., 1802, ABH KONIGL BOHM GES
[8]  
Goyon R., 1958, ANN FS U TOULOUSE, V22, P1, DOI DOI 10.5802/AFST.482
[9]   Global continuation in nonlinear elasticity [J].
Healey, TJ ;
Simpson, HC .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1998, 143 (01) :1-28
[10]   EXISTENCE THEORY FOR IR-ROTATIONAL WATER-WAVES [J].
KEADY, G ;
NORBURY, J .
MATHEMATICAL PROCEEDINGS OF THE CAMBRIDGE PHILOSOPHICAL SOCIETY, 1978, 83 (JAN) :137-157
123