In this article, we derive explicit asymptotic formulas for the solutions of Oseen's equations in space dimension two in a channel at large Reynolds number (small viscosity ε). These formulas exhibit typical boundary layers behaviors. Suitable correctors are defined to resolve the boundary obstacle and obtain convergence results valid up to the boundary. We study also the behavior of the boundary layer when simultaneously time and the Reynolds number tend to infinity in which case the boundary layer tends to pervade the whole domain.
R. Temam and X. Wang, "Asymptotic Analysis of Oseen Equations for Small Viscosity," Applied Mathematics Letters, vol. 9, no. 2, pp. 1 - 4, Elsevier, Jan 1996.
The definitive version is available at https://doi.org/10.1016/0893-9659(96)00001-8
Mathematics and Statistics
Keywords and Phrases
Asymptotic Expansions; Boundary Layer; Correctors; Navier-Stokes Equations; Oseen's Equations
International Standard Serial Number (ISSN)
Article - Journal
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01 Jan 1996
National Science Foundation, Grant NSF-DMS-9400615