Stability and instability of Navier boundary layers

Matthew Paddick

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arXiv · 1103.5009

Stability and instability of Navier boundary layers

Matthew Paddick

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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 WKB expansions in the stronger $L^{\infty}$ and $\dot{H}^s$ (s>1) norms.

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Matthew Paddick. 2014-12-10. Stability and instability of Navier boundary layers. https://arxiv.org/abs/1103.5009

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