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September/October 2014 Stability and instability of Navier boundary layers
Matthew Paddick
Differential Integral Equations 27(9/10): 893-930 (September/October 2014).

Abstract

We study the inviscid limit problem for the incompressible Navier-Stokes equation on a half-plane with a Navier boundary condition depending on the viscosity. On one hand, we prove the $L^{2}$ convergence of Leray solutions to the solution of the Euler equation. On the other hand, we show the nonlinear instability of some WKB expansions in the stronger $L^{\infty}$ and $\dot{H}^{s}$ ($s>1$) norms. These results are not contradictory, and in the periodic setting, we provide an example for which both phenomena occur simultaneously.

Citation

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Matthew Paddick. "Stability and instability of Navier boundary layers." Differential Integral Equations 27 (9/10) 893 - 930, September/October 2014.

Information

Published: September/October 2014
First available in Project Euclid: 1 July 2014

zbMATH: 1340.35249
MathSciNet: MR3229096

Subjects:
Primary: 35Q30, 76D10

Rights: Copyright © 2014 Khayyam Publishing, Inc.

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Vol.27 • No. 9/10 • September/October 2014
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