Regularity and symmetry properties of rotational solitary water waves

被引：13

作者：

Matioc, Anca-Voichita ^{[1
]}

Matioc, Bogdan-Vasile ^{[1
]}

机构：

[1] Univ Vienna, Inst Math, A-1090 Vienna, Austria

来源：

JOURNAL OF EVOLUTION EQUATIONS | 2012年 / 12卷 / 02期

基金：

奥地利科学基金会;

关键词：

Solitary wave; Symmetry; Real-analytic; Maximum principles; VORTICITY; ANALYTICITY; AMPLITUDE; EQUATIONS; BOUNDARY; STOKES;

D O I：

10.1007/s00028-012-0141-7

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We prove that a solitary water wave driven by gravity has real-analytic streamlines for arbitrary vorticity functions if the flow contains no stagnation points. Based on this property, we show that if all the streamlines attain their global maximum (resp. minimum) on the same vertical line, then the solitary wave has to be symmetric and strictly monotone away from the crest (resp. trough). Our results are true for sub- and supercritical solitary waves as well.

引用

页码：481 / 494

页数：14

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