Abstract In this work, we establish the convergence of 2D, stationary Navier-Stokes flows with viscosity > 0, (u^, v^) to the classical Prandtl boundary layer, (uₚ, vₚ), posed on the domain (0, ) (0, ): align* \| u^ - uₚ \|₋^㶆 x ^- 1 4 +, \| v^ - vₚ \|₋^㶆 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 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.
Iyer et al. (Thu,) studied this question.