In this three-part monograph, we prove that steady, incompressible Navier-Stokes flows posed over the moving boundary, y = 0, can be decomposed into Euler and Prandtl flows in the inviscid limit globally in [1, ∞) × [0, ∞), assuming a sufficiently small velocity mismatch. Sharp decay rates and self-similar asymptotics are extracted for both Prandtl and Eulerian layers. We then develop a functional framework to capture precise decay rates of the remainders, and prove the corresponding embedding theorems by establishing weighted estimates for their higher order tangential derivatives. These tools are then used in conjunction with a third order energy analysis, which in particular enables us to control the nonlinearity vu y globally.

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We characterize the well known self-similar Blasius profiles, [ū,v], as downstream attractors to solutions [u, v] to the 2D, stationary Prandtl system. It was established inOur result furthers [Ser66] in the case of localized data near Blasius by establishing convergence in stronger norms and by characterizing the decay rates. Central to our analysis is a "division estimate", in turn based on the introduction of a new quantity, Ω, which is globally nonnegative precisely for Blasius solutions. Coupled with an energy cascade and a new weighted Nash-type inequality, these ingredients yield convergence of u −ū and v −v at the essentially the sharpest expected rates in W k,p norms.