SOLVABILITY OF THE FREE BOUNDARY VALUE PROBLEM OF THE NAVIER-STOKES EQUATIONS

被引：28

作者：

Bae, Hantaek ^{[1
]}

机构：

[1] Univ Maryland, Ctr Sci Computat & Math Modeling, College Pk, MD 20742 USA

来源：

DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS | 2011年 / 29卷 / 03期

关键词：

Navier-Stokes equations; Free Boundary; Surface Tension; WATER-WAVE PROBLEM; WELL-POSEDNESS; SOBOLEV SPACES;

D O I：

10.3934/dcds.2011.29.769

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we study the incompressible Navier-Stokes equations on a moving domain in R-3 of finite depth, bounded above by the free surface and bounded below by a solid flat bottom. We prove that there exists a unique, global-in-time solution to the problem provided that the initial velocity field and the initial profile of the boundary are sufficiently small in Sobolev spaces.

引用

页码：769 / 801

页数：33

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