International Journal of Stochastic Analysis

International Journal of Stochastic Analysis / 2000 / Article

Open Access

Volume 13 |Article ID 679124 | 17 pages | https://doi.org/10.1155/S1048953300000241

Analyzing the dynamics of the forced Burgers equation

Received01 Apr 1998
Revised01 Oct 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+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.

Copyright © 2000 Hindawi Publishing Corporation. 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.

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