Analyzing the dynamics of the forced Burgers equation (Q1841233)

Summary: We study numerically the long-time dynamics of a system of reaction-diffusion equations that arise from the viscous forced Burgers equation \((u_t + uu_x-\nu u_{xx}= F\)). A nonlinear transformation introduced by \textit{M. Kwak} [Indiana Univ. Math. J. 41, No.~4, 927-981 (1992; Zbl 0765.35034)] 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 \(\nu\).