Stability and instability of Navier boundary layers

Stabilité et instabilité de couches limites pour condition de Navier

Matthew Paddick (1)

1 IRMAR - Institut de Recherche Mathématique de Rennes

We study the inviscid limit problem for the incompressible Navier-Stokes equa-tion 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 ∞ and ˙ 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.

Mots clés: inviscid limit problem; nonlinear instability; Navier boundary condition; boundary layers

Domaines: Mathématiques [math]; Equations aux dérivées partielles [math.AP]; Physique mathématique [math-ph]

Matthew Paddick. Stability and instability of Navier boundary layers. Differential and integral equations, 2014, 27 (9-10), pp.893-930. ⟨hal-01093331⟩