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.
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页码：769 / 801
页数：33
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