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Orr-Sommerfeld equation and complex deformation

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arxiv 2503.22274 v2 pith:EJXZHCMV submitted 2025-03-28 math.AP

Orr-Sommerfeld equation and complex deformation

Malo J\'ez\'equel , Jian Wang This is my paper
classification math.AP
keywords equationcomplexdeformationrayleighresonancesshearanalyticityassumption
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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 Rayleigh equation is considered. We show such resonances are inviscid limits of the eigenvalues of the corresponding Orr--Sommerfeld equation.

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