LARGE-AMPLITUDE SOLITARY WATER WAVES WITH VORTICITY

被引：26
作者：
Wheeler, Miles H. [1 ]
机构：
[1] Brown Univ, Dept Math, Providence, RI 02912 USA
来源：
SIAM JOURNAL ON MATHEMATICAL ANALYSIS | 2013年 / 45卷 / 05期
关键词：
water waves; vorticity; solitary waves; ARBITRARY DISTRIBUTION; DIFFERENTIAL-EQUATIONS; ELLIPTIC-EQUATIONS; STOKES CONJECTURE; GREATEST HEIGHT; EXISTENCE; FREDHOLM; SYMMETRY; BOUNDARY;
D O I：
10.1137/120891460
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We provide the first construction of exact solitary waves of large amplitude with an arbitrary distribution of vorticity. We use continuation to construct a global connected set of symmetric solitary waves of elevation, whose profiles decrease monotonically on either side of a central crest. This generalizes the classical result of Amick and Toland.
引用
收藏
页码：2937 / 2994
页数：58
相关论文
共 49 条
[1]   ESTIMATES NEAR THE BOUNDARY FOR SOLUTIONS OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS SATISFYING GENERAL BOUNDARY CONDITIONS .1. [J].
AGMON, S ;
DOUGLIS, A ;
NIRENBERG, L .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1959, 12 (04) :623-727
[2]   ON PERIODIC WATER-WAVES AND THEIR CONVERGENCE TO SOLITARY WAVES IN THE LONG-WAVE LIMIT [J].
AMICK, CJ ;
TOLAND, JF .
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1981, 303 (1481) :633-669
[3]  
AMICK CJ, 1981, ARCH RATION MECH AN, V76, P9, DOI 10.1007/BF00250799
[4]  
BEALE JT, 1977, COMMUN PUR APPL MATH, V30, P373
[5]   THE SOLITARY WAVE ON A STREAM WITH AN ARBITRARY DISTRIBUTION OF VORTICITY [J].
BENJAMIN, TB .
JOURNAL OF FLUID MECHANICS, 1962, 12 (01) :97-116
[6]   SOLITARY-WAVE SOLUTIONS OF NONLINEAR PROBLEMS [J].
BENJAMIN, TB ;
BONA, JL ;
BOSE, DK .
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY OF LONDON SERIES A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1990, 331 (1617) :195-244
[7]  
Burns J. C., 1953, MATH P CAMBRIDGE PHI, V49, P695
[8]  
Coddington E. A., 1955, THEORY ORDINARY DIFF
[9]   Exact steady periodic water waves with vorticity [J].
Constantin, A ;
Strauss, W .
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 2004, 57 (04) :481-527
[10]   Periodic Traveling Gravity Water Waves with Discontinuous Vorticity [J].
Constantin, Adrian ;
Strauss, Walter .
ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 2011, 202 (01) :133-175
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