VANISHING VISCOSITY PLANE PARALLEL CHANNEL FLOW AND RELATED SINGULAR PERTURBATION PROBLEMS

We study a special class of solutions to the three-dimensional Navier–Stokes equations (Formula Presented), with no-slip boundary condition, on a domain of the form (Formula Presented), dealing with velocity fields of the form (Formula Presented), describing plane-parallel channel flows. We establish results on convergence (Formula Presented), where u⁰ solves the associated Euler equations. These results go well beyond previously established L²-norm convergence, and provide a much more detailed picture of the nature of this convergence. Carrying out this analysis also leads naturally to consideration of related singular perturbation problems on bounded domains.