On the L^(∞) stability of Prandtl expansions in the Gevrey class  

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》2022年第12期2521-2562,共42页中国科学：数学（英文版）

摘　　要：In this paper, we prove the L^(∞)∩ L^(2) stability of Prandtl expansions of the shear flow type as(U(y/ν1/2), 0)for the initial perturbation in the Gevrey class, where U(y) is a monotone and concave function and ν is the viscosity coefficient. To this end, we develop the direct resolvent estimate method for the linearized Orr-Sommerfeld operator instead of the Rayleigh-Airy iteration method. Our method could be applied to the other relevant problems of hydrodynamic stability.

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

分 类 号：O35[理学—流体力学]