A remark on the existence of steady Navier-Stokes flows in 2D semi-infinite channel involving the general outflow condition

Morimoto, H., and Fujita, H.. "A remark on the existence of steady Navier-Stokes flows in 2D semi-infinite channel involving the general outflow condition." Mathematica Bohemica 126.2 (2001): 457-468. <http://eudml.org/doc/248832>.

@article{Morimoto2001,
abstract = {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 < 0 \rbrace $ is bounded and 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.},
author = {Morimoto, H., Fujita, H.},
journal = {Mathematica Bohemica},
keywords = {stationary Navier-Stokes equations; non-vanishing outflow; 2-dimensional semi-infinite channel; symmetry; stationary Navier-Stokes equations; non-vanishing outflow; 2-dimensional semi-infinite channel; symmetry},
language = {eng},
number = {2},
pages = {457-468},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {A remark on the existence of steady Navier-Stokes flows in 2D semi-infinite channel involving the general outflow condition},
url = {http://eudml.org/doc/248832},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Morimoto, H.
AU - Fujita, H.
TI - A remark on the existence of steady Navier-Stokes flows in 2D semi-infinite channel involving the general outflow condition
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 2
SP - 457
EP - 468
AB - 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 < 0 \rbrace $ is bounded and 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.
LA - eng
KW - stationary Navier-Stokes equations; non-vanishing outflow; 2-dimensional semi-infinite channel; symmetry; stationary Navier-Stokes equations; non-vanishing outflow; 2-dimensional semi-infinite channel; symmetry
UR - http://eudml.org/doc/248832
ER -