Shear Flows of an Ideal Fluid and Elliptic Equations in Unbounded Domains
Shear Flows of an Ideal Fluid and Elliptic Equations in Unbounded Domains
复制标题
无界域中理想流体的剪切流和椭圆方程
DOI：
--
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
N. Nadirashvili
中科院分区：
文献类型：
--
作者：
F. Hamel;N. Nadirashvili
我们证明，在二维条带中，没有驻点和切向边界条件的理想不可压缩流体的稳定流动是剪切流。同样的结论也适用于半平面内的有界稳定流。证明基于对流动流线几何性质的研究以及一些半线性椭圆方程解的一维对称性结果。一些独立感兴趣的相关刚性结果也显示在任何维度 n 的 n 维板中。© 2016 Wiley periodicals, Inc.
We prove that, in a two‐dimensional strip, a steady flow of an ideal incompressible fluid with no stationary point and tangential boundary conditions is a shear flow. The same conclusion holds for a bounded steady flow in a half‐plane. The proofs are based on the study of the geometric properties of the streamlines of the flow and on one‐dimensional symmetry results for solutions of some semilinear elliptic equations. Some related rigidity results of independent interest are also shown in n‐dimensional slabs in any dimension n.© 2016 Wiley Periodicals, Inc.