Abstract
In this paper, we study the stability of shear flows of Prandtl type as $$\left({U\left({y/\sqrt \nu} \right),0} \right)$$ 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.
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