Steady Prandtl layer expansions with external forcing

In this article we apply the machinery developed by Guo and Iyer [Validity of Steady Prandtl Layer Expansions, Comm. Pure Appl. Math. (to appear) (2022)] together with a new compactness estimate quantity, “degree”, in order to prove validity steady layer expansions external forcing. The techniques introduced allow us treat more general background layers than (2022)].