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December 2002 A Remark on the Existence of Steady Navier-Stokes Flows in a Certain Two-Dimensional Infinite Channel
Hiroshi FUJITA, Hiroko MORIMOTO
Tokyo J. Math. 25(2): 307-321 (December 2002). DOI: 10.3836/tjm/1244208856

Abstract

We consider the steady Navier-Stokes equations $$ \left\{ \begin{array}{@{}l@{\hspace{2pt}}ll} (\mathbf{u}\cdot\nabla)\mathbf{u} & =\nu \Delta\mathbf{u} -\nabla p & \text{in}~\Omega\,,\\ \text{div}\,\mathbf{u} & =0 & \text{in} ~\Omega\,, \end{array} \right. $$ in a 2-dimensional unbounded multiply-connected domain $\Omega$ contained in an infinite straight channel $\mathbf{R}\times(-1,1)$, under general outflow condition. We look for a solution which tends to a Poiseuille flow at infinity. In this note, we shall show the existence of solution to this problem under the assumption of symmetry with respect to the axis for the domain and the boundary value, and for small Poiseuille flow. We do not assume that the boundary value is small. The regularity and the asymptotic behavior of the solution are also discussed.

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Hiroshi FUJITA. Hiroko MORIMOTO. "A Remark on the Existence of Steady Navier-Stokes Flows in a Certain Two-Dimensional Infinite Channel." Tokyo J. Math. 25 (2) 307 - 321, December 2002. https://doi.org/10.3836/tjm/1244208856

Information

Published: December 2002
First available in Project Euclid: 5 June 2009

zbMATH: 1042.35049
MathSciNet: MR1948667
Digital Object Identifier: 10.3836/tjm/1244208856

Subjects:
Primary: 35Q30
Secondary: 76D03, 76D05

Rights: Copyright © 2002 Publication Committee for the Tokyo Journal of Mathematics

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Vol.25 • No. 2 • December 2002
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