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

Abstract

In this paper, we prove the stability of shear flows of Prandtl type as $(U(y/\sqrt{\nu }),0)$ for the steady Navier-Stokes equations under a natural spectral assumption on the linearized NS operator. We develop a direct energy method combined with compact method to solve the Orr-Sommerfeld equation.