Orr--Sommerfeld equation and complex deformation

Orateur:	Jian Wang (IHES)
Localisation:
Type:	Groupe de travail équations aux dérivées partielles
Site:	P4 423
Salle:	La salle du conseil
Date de début:	09/10/2025 - 13:45
Date de fin:	09/10/2025 - 14:45

Abstract: For shear flows in a 2D channel, we define resonances near regular values of the shear profile for the Rayleigh equation under an analyticity assumption. This is done via complex deformation of the interval on which the Rayleigh equation is considered. We show such resonances are inviscid limits of the eigenvalues of the corresponding Orr–Sommerfeld equation. We also present explicit examples where viscous perturbations of resonances become unstable eigenvalues. Joint work with Malo Jézéquel.