Green function for linearized Navier-Stokes around a boundary shear layer profile for long wavelengths

2019/10/09 by Grenier, Emmanuel, Nguyen, Toan T.
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1910.03988

Abstract

This paper is the continuation of a program, initiated in Grenier-Nguyen [8,9], to derive pointwise estimates on the Green function of Orr Sommerfeld equations. In this paper we focus on long wavelength perturbations, more precisely horizontal wavenumbers α of order ν^1/4, which correspond to the lower boundary of the instability area for monotonic profiles.

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• Green function for linearized Navier-Stokes around a boundary layer profile: near critical layers
• Green function of Orr Sommerfeld equations away from critical layers
• Pointwise Green function bounds and long-time stability of large-amplitude noncharacteristic boundary layers
• Asymptotic behaviour of solutions of linearized Navier Stokes equations in the long waves regime
• Stability of shear flows near a boundary