The goal of this article is to study the boundary layer for a flow in a channel with permeable walls. Observing that the Prandtl equation can be solved almost exactly in this case, we are able to derive rigorously a number of results concerning the boundary layer and the convergence of the Navier-Stokes equations to the Euler equations. We indicate also how to derive higher order terms in the inner and outer expansions with respect to the kinematic viscosity v.
R. Temam and X. Wang, "Remarks on the Prandtl Equation for a Permeable Wall," ZAMM Zeitschrift fur Angewandte Mathematik und Mechanik, vol. 80, no. 11 thru 12, pp. 835 - 843, Wiley, Jan 2000.
The definitive version is available at https://doi.org/10.1002/1521-4001(200011)80:11/12<835::aid-zamm835>3.0.co;2-9
Mathematics and Statistics
Keywords and Phrases
Boundary Layers; Euler Equations; Fluid Mechanics; Navier-Stokes Equations; Prandtl Equations; Vanishing Viscosity
International Standard Serial Number (ISSN)
Article - Journal
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01 Jan 2000