Electronic Journal of Differential Equations,
Conference 01 (1998), pp. 149-160.

Title: On the Existence of Steady Flow in a Channel with one Porous Wall or Two Accelerating Walls 


Authors: Chunqing Lu (Southern Illinois Univ., Edwardsville, Illinois, USA)

 
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
$F(-1)=F'(-1)=F'(1)=0$, $F(1)=-1$.
In the latter case, the boundary conditions are $F(-1)=F(1)=0$, $F'(-1)=-1$,
$F'(1) = 1$.



Published November 12, 1998.
Math Subject Classifications: 34B15, 76D05.
Key Words: laminar flow; similarity solutions; Navier-Stokes equations.