Stability of the Favorable Falkner-Skan Profiles for the Stationary Prandtl Equations

Abstract: The (favorable) Falkner-Skan boundary layer profiles are a one parameter ($\beta \in [0,2]$) family of self-similar solutions to the stationary Prandtl system which describes the flow over a wedge with angle $\beta \frac{\pi}{2}$. The most famous member of this family is the endpoint Blasius profile, $\beta = 0$, which exhibits pressureless flow over a flat plate. In contrast, the $\beta > 0$ profiles are physically expected to exhibit a \textit{favorable pressure gradient}, a common adage in the physics literature. In this work, we prove quantitative scattering estimates as $x \rightarrow \infty$ which precisely captures the effect of this favorable gradient through the presence of new ``CK" (Cauchy-Kovalevskaya) terms that appear in a quasilinear energy cascade.