The Zero Surface Tension Limit of Three-dimensional Water Waves

被引：70

作者：

Ambrose, David M. ^{[1
]}

Masmoudi, Nader ^{[2
]}

机构：

[1] Clemson Univ, Dept Math Sci, Clemson, SC 29634 USA

[2] NYU, Courant Inst Math Sci, New York, NY 10012 USA

来源：

INDIANA UNIVERSITY MATHEMATICS JOURNAL | 2009年 / 58卷 / 02期

基金：

美国国家科学基金会;

关键词：

BOUNDARY INTEGRAL METHOD; INCOMPRESSIBLE IDEAL FLUID; WELL-POSEDNESS; EULER-EQUATIONS; VORTEX SHEETS; SOBOLEV SPACES; 3-D; CONVERGENCE; MOTION; FLOW;

D O I：

10.1512/iumj.2009.58.3450

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We establish that the limit of the water wave with surface tension, as surface tension vanishes, is the water wave without surface tension. The main tool is an energy estimate which is uniform in the surface tension parameter. Before establishing estimates, we reformulate the problem using suitable variables and an isothermal parameterization. With these variables and parameterizations, estimates for the water wave with or without surface tension are straightforward. In particular, this provides a new proof of existence of irrotational water waves in three space dimensions.

引用

页码：479 / 521

页数：43

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