A remark on the existence of steady Navier-Stokes flows in 2D semi-infinite channel involving the general outflow condition
A remark on the existence of steady Navier-Stokes flows in 2D semi-infinite channel involving the general outflow condition
复制标题
涉及一般流出条件的二维半无限通道中稳态纳维-斯托克斯流存在性的评述
DOI：
10.21136/mb.2001.134017
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发表时间：
2001
影响因子：
0.6
通讯作者：
H. Fujita
中科院分区：
文献类型：
--
作者：
H. Morimoto;H. Fujita
在一般流出条件下，我们考虑二维无界多连通区域中定常的Navier-Stokes方程。设$T$是二维直线通道$\mathbb{R}\x(-1，1)$。我们假设$\Omega\Cap\lbrace x_1-1\rbrace=T\Cap\lbrace x_1>；-1\rbrbrace$。设$V$是$T$中的Poiseuille流，$\Mu$是$V$的流量。我们寻找一个趋向于$V$作为$x_1\right tarrow\inty$的解。假设区域和边界数据关于$x_1$轴是对称的，且该轴与边界的每个分量相交，我们证明了当通量很小时解的存在性(Morimoto-Fujita[8])。本笔记中将报告一些改进。我们还证明了解的某些正则性和渐近性质。
We consider the steady Navier-Stokes equations in a 2-dimensional unbounded multiply connected domain $\Omega $ under the general outflow condition. Let $T$ be a 2-dimensional straight channel $\mathbb{R} \times (-1,1)$. We suppose that $\Omega \cap \lbrace x_1 -1 \rbrace = T \cap \lbrace x_1 > -1 \rbrace $. Let $V$ be a Poiseuille flow in $T$ and $\mu $ the flux of $V$. We look for a solution which tends to $V$ as $x_1 \rightarrow \infty $. Assuming that the domain and the boundary data are symmetric with respect to the $x_1$-axis, and that the axis intersects every component of the boundary, we have shown the existence of solutions if the flux is small (Morimoto-Fujita [8]). Some improvement will be reported in this note. We also show certain regularity and asymptotic properties of the solutions.