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

In this paper, we study the stability of shear flows of Prandtl type as (U(y/root nu), 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.

Automated summary

This paper studies the stability of shear flows of Prandtl type in the steady Navier-Stokes equations and employs a direct energy method combined with the compactness method to solve the problem.