Stability and instability of Navier boundary layers

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.

Cited by in corpus (3)

• Instability of Boundary Layers with the Navier Boundary Condition
• Transverse nonlinear instability of Euler-Korteweg solitons
• On convergence criteria for incompressible Navier-Stokes equations with Navier boundary conditions and physical slip rates