Long-wave instabilities

Dongfen Bian; Emmanuel Grenier

doi:10.1007/s11425-022-2148-2

Long-wave instabilities

Dongfen Bian, Emmanuel Grenier^*

^*Corresponding author for this work

School of Mathematics and Statistics

Unité de Mathématiques Pures et Appliquées de l'ENS de Lyon

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

This paper aims to give a detailed presentation of long-wave instabilities of shear layers for Navier-Stokes equations, and in particular to give a simple and easy-to-read presentation of the study of the Orr-Sommerfeld equation and to detail the analysis of its adjoint. Using these analyses, we prove the existence of long-wave instabilities in the cases of slowly rotating fluids, slightly compressible fluids or Navier boundary conditions, under smallness conditions.

Original language	English
Pages (from-to)	1761-1776
Number of pages	16
Journal	Science China Mathematics
Volume	67
Issue number	8
DOIs	https://doi.org/10.1007/s11425-022-2148-2
Publication status	Published - Aug 2024

Keywords

Navier-Stokes equations
Prandtl equations
boundary layers

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10.1007/s11425-022-2148-2

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Bian, D., & Grenier, E. (2024). Long-wave instabilities. Science China Mathematics, 67(8), 1761-1776. https://doi.org/10.1007/s11425-022-2148-2

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author = "Dongfen Bian and Emmanuel Grenier",

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N2 - This paper aims to give a detailed presentation of long-wave instabilities of shear layers for Navier-Stokes equations, and in particular to give a simple and easy-to-read presentation of the study of the Orr-Sommerfeld equation and to detail the analysis of its adjoint. Using these analyses, we prove the existence of long-wave instabilities in the cases of slowly rotating fluids, slightly compressible fluids or Navier boundary conditions, under smallness conditions.

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Long-wave instabilities

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Keywords

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