Differential Equations and Computational Simulations III
Electron. J. Diff. Eqns., Conf. 01, 1997, pp. 159-170.

On the existence of steady flow in a channel with one porous wall or two accelerating walls

Chunqing Lu

Abstract:
This paper presents a rigorous proof of the existence of steady flows in a channel either with no-slip at one wall and constant uniform suction or injection through another wall, or with two accelerating walls. The flows are governed by the fourth order nonlinear differential equation
$$F^{iv}+R(FF'''-F'F'')=0\,.$$
In the former case, the flow is subject to the boundary conditions
$$F(-1)=F'(-1)=F'(1)=0,\quad F(1)=-1\,.$$
In the latter case, the boundary conditions are
$$F(-1)=F(1)=0,\quad F'(-1)=-1, \quad F'(1) = 1\,.$$

Published November 12, 1998.
Mathematics Subject Classifications: 34B15, 76D05.
Key words and phrases: laminar flow, similarity solutions, Navier-Stokes equations.

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Chunqing Lu
Department of Mathematics and Statistics
Southern Illinois University at Edwardsville
Edwardsville, Illinois 62026, USA
Email address: clu@siue.edu
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