Global inviscid limit of 2D, stationary Navier-Stokes and stability of Prandtl expansions

In this work, we establish the convergence of 2D, stationary Navier-Stokes flows with viscosity ε> 0 , (u^ε , v^ε ) to the classical Prandtl boundary layer, (ūₚ, v̄ₚ) , posed on the domain (0, ∞ ) × (0, ∞ ) : $$ {align*} \| u^ε - ū_p \|L^∞_y √ε x - 1 4 + δ, \| v^ε - √ε v̄_p \|L^∞_y √ε x - 1 2. {align*} $$ This validates Prandtl’s boundary layer theory globally in the x -variable for a large class of boundary layers, including the entire one parameter family of the classical Blasius profiles, with sharp decay rates. The result demonstrates asymptotic stability in two senses simultaneously: (1) asymptotic as ε → 0 and (2) asymptotic as x → ∞ . In particular, our result provides the first rigorous confirmation for the Navier-Stokes equations that the boundary layer cannot “separate” in these stable regimes, which is very important for physical and engineering applications.