Global Steady Prandtl Expansion over a Moving Boundary III

Abstract

This is the third paper in a three-part sequence 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 paper, we prove existence and uniqueness of solutions to the remainder equation.