On the stability of shear flows of Prandtl type for the steady Navier-Stokes equations  

作　　者：Qi Chen Di Wu Zhifei Zhang 

机构地区：[1]School of Mathematical Sciences,Peking University,Beijing 100871,China [2]School of Mathematics,South China University of Technology,Guangzhou 510641,China

出　　处：《Science China Mathematics》2023年第4期679-722,共44页中国科学：数学（英文版）

基　　金：supported by National Natural Science Foundation of China(Grant No.12101245);supported by National Natural Science Foundation of China(Grant No.12171010)。

摘　　要：In this paper, we study the stability of shear flows of Prandtl type as(U(y/√ν), 0) for the steady Navier-Stokes equations under a natural spectral assumption on the linearized NS operator. The key ingredient is to solve the Orr-Sommerfeld equation. For this, we develop a direct energy method combined with the compactness method, which may be of independent interest.

关 键 词：Navier-Stokes equations shear flow Prandtl expansion 

分 类 号：O175[理学—数学]