Long-wave instabilities  

作　　者：Dongfen Bian Emmanuel Grenier 

机构地区：[1]School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 100081,China [2]Unité de Mathématiques Pures et Appliquées,CNRS UMR 5669,Ecole Normale Supérieure de Lyon,Lyon 69007,France

出　　处：《Science China Mathematics》2024年第8期1761-1776,共16页中国科学（数学）（英文版）

基　　金：supported by National Natural Science Foundation of China (Grant Nos. 11871005 and 12271032)。

摘　　要：This paper aims to give a detailed presentation of long-wave instabilities of shear layers for NavierStokes equations,and in particular to give a simple and easy-to-read presentation of the study of the OrrSommerfeld 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 fuids,slightly compressible fuids,or fuids with Navier boundary conditions,under smallness conditions.

关 键 词：Navier-Stokes equations boundary layers Prandtl equations 

分 类 号：O175[理学—数学]