Analyzing the dynamics of the forced Burgers equation
We study numerically the long-time dynamics of a system of reaction-diffusion equations that arise from the viscous forced Burgers equation . 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 .