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

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
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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