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

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

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.