A remark on a Liouville problem with boundary for the Stokes and the Navier-Stokes equations
A remark on a Liouville problem with boundary for the Stokes and the Navier-Stokes equations
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关于具有斯托克斯和纳维-斯托克斯方程边界的刘维尔问题的评论
DOI：
10.3934/dcdss.2013.6.1277
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发表时间：
2011
影响因子：
2.4
通讯作者：
Y. Giga
中科院分区：
文献类型：
--
作者：
Y. Giga
构造了半空间中非定常Navier-Stokes方程和Stokes方程的有界全解的Poiseuille型流。特别地，我们的结果表明，在无滑移边界条件下，Liouville问题存在一个非平凡解。对整个空间和滑移边界条件的情况进行了回顾。2000数学学科分类。主:35 q30;次级：35B40、76D05、76D07。
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. 2000 Mathematics Subject Classification. Primary: 35Q30; Secondary: 35B40, 76D05, 76D07.