Journal of Applied Mathematics and Stochastic Analysis
Volume 13 (2000), Issue 3, Pages 269-285

Analyzing the dynamics of the forced Burgers equation

Nejib Smaoui

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.


We study numerically the long-time dynamics of a system of reaction-diffusion equations that arise from the viscous forced Burgers equation (ut+uuxvuxx=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.