Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 3, Pages 269-285
doi:10.1155/S1048953300000241
Analyzing the dynamics of the forced Burgers equation
Kuwait University, Department of Mathematics and Computer Science, P.O. Box 5969, Safat 13060, Kuwait
Received 1 April 1998; Revised 1 October 1999
Copyright © 2000 Nejib Smaoui. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We study numerically the long-time dynamics of a system of reaction-diffusion equations that arise from the viscous forced Burgers equation (ut+uux−vuxx=F). A nonlinear transformation introduced by Kwak is used
to embed the scalar Burgers equation into a system of reaction diffusion
equations. The Kwak transformation is used to determine the existence of
an inertial manifold for the 2-D Navier-Stokes equation. We show
analytically as well as numerically that the two systems have a similar,
long-time dynamical, behavior for large viscosity v.