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
Matthew Paddick. "Stability and instability of Navier boundary layers." Differential Integral Equations 27 (9/10) 893 - 930, September/October 2014. https://doi.org/10.57262/die/1404230050
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