Global Steady Prandtl Expansion over a Moving Boundary I

Abstract

This is the first of three papers in which 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 $[1, \infty ) \times [0,\infty )$, assuming a sufficiently small velocity mismatch. In this part, sharp decay rates and self-similar asymptotics are extracted for both Prandtl and Eulerian layers.