Abstract
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) |
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Pages (from-to) | 35-93 |
Number of pages | 59 |
Journal | Analysis and PDE |
Volume | 1 |
Issue number | 1 |
DOIs | |
State | Published - 2008 |
All Science Journal Classification (ASJC) codes
- Analysis
- Numerical Analysis
- Applied Mathematics