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Title: A remark on the existence of steady Navier-Stokes flows in 2D semi-infinite channel involving the general outflow condition (English)
Author: Morimoto, H.
Author: Fujita, H.
Language: English
Journal: Mathematica Bohemica
ISSN: 0862-7959 (print)
ISSN: 2464-7136 (online)
Volume: 126
Issue: 2
Year: 2001
Pages: 457-468
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: stationary Navier-Stokes equations
Keyword: non-vanishing outflow
Keyword: 2-dimensional semi-infinite channel
Keyword: symmetry
MSC: 35B40
MSC: 35B65
MSC: 35Q30
MSC: 76D03
MSC: 76D05
idZBL: Zbl 0981.35049
idMR: MR1844283
DOI: 10.21136/MB.2001.134017
Date available: 2009-09-24T21:52:42Z
Last updated: 2020-07-29
Stable URL:
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Reference: [4] Fujita, H.: On stationary solutions to Navier-Stokes equations in symmetric plane domains under general out-flow condition.Proceedings of International Conference on Navier-Stokes Equations, Theory and Numerical Methods, June 1997, Varenna Italy, Pitman Reseach Notes in Mathematics 388, pp. 16–30. MR 1773581
Reference: [5] Galdi, G. P.: An Introduction to the Mathematical Theory of the Navier-Stokes Equations.Springer, 1994. Zbl 0949.35005
Reference: [6] Ladyzhenskaya, O. A.: The Mathematical Theory of Viscous Incompressible Flow.Gordon and Breach, New York, 1969. Zbl 0184.52603, MR 0254401
Reference: [7] Morimoto, H., Fujita, H.: A remark on existence of steady Navier-Stokes flows in a certain two dimensional infinite tube.Technical Reports Dept. Math., Math-Meiji 99-02, Meiji Univ.
Reference: [8] Morimoto, H., Fujita, H.: On stationary Navier-Stokes flows in 2D semi-infinite channel involving the general outflow condition.NSEC7, Ferrara, Italy,.


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