The Lifespan of Small Data Solutions in Two Dimensional Capillary Water Waves

被引：60

作者：

Ifrim, Mihaela ^{[1
]}

Tataru, Daniel ^{[1
]}

机构：

[1] Univ Calif Berkeley, Dept Math, Berkeley, CA 94720 USA

来源：

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS | 2017年 / 225卷 / 03期

关键词：

CONDITIONAL ENERGETIC STABILITY; NONLINEAR SCHRODINGER-EQUATION; KLEIN-GORDON EQUATIONS; SURFACE-TENSION; WELL-POSEDNESS; GLOBAL-SOLUTIONS; SOBOLEV SPACES; IDEAL FLUID; EXISTENCE; MOTION;

D O I：

10.1007/s00205-017-1126-z

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This article is concerned with the incompressible, irrotational infinite depth water wave equation in two space dimensions, without gravity but with surface tension. We consider this problem expressed in position-velocity potential holomorphic coordinates, and prove that small data solutions have at least cubic lifespan while small localized data leads to global solutions.

引用

页码：1279 / 1346

页数：68

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