A REMARK ON A LIOUVILLE PROBLEM WITH BOUNDARY FOR THE STOKES AND THE NAVIER-STOKES EQUATIONS

被引：7
|
作者：
Giga, Yoshikazu [1 ,2 ]
机构：
[1] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, Tokyo 1538914, Japan
[2] King Abdulaziz Univ, Fac Sci, Dept Math, Jeddah 21589, Saudi Arabia
来源：
DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S | 2013年 / 6卷 / 05期
基金：
日本学术振兴会;
关键词：
Liouville problem; Navier-Stokes equations; non-slip boundary condition; Poiseuille type flow; THEOREMS; EULER; REGULARITY;
D O I：
10.3934/dcdss.2013.6.1277
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We construct a Poiseuille type flow which is a bounded entire solution of the nonstationary Navier-Stokes and the Stokes equations in a half space with non-slip boundary condition. Our result in particular implies that there is a nontrivial solution for the Liouville problem under the non-slip boundary condition. A review for cases of the whole space and a slip boundary condition is included.
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页码：1277 / 1289
页数：13
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