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.
|Original language||English (US)|
|Number of pages||59|
|Journal||Analysis and PDE|
|State||Published - 2008|
All Science Journal Classification (ASJC) codes
- Numerical Analysis
- Applied Mathematics