2024/03/12 by Sameer Iyer, Iyer, Sameer
Mathematics · #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods for differential equations #Numerical methods in inverse problems
paper · pdf · doi:10.48550/arxiv.2403.07791
openalex publication_date 2024/03/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The (favorable) Falkner-Skan boundary layer profiles are a one parameter (β∈ [0,2]) family of self-similar solutions to the stationary Prandtl system which describes the flow over a wedge with angle β\fracπ2. The most famous member of this family is the endpoint Blasius profile, β= 0, which exhibits pressureless flow over a flat plate. In contrast, the β> 0 profiles are physically expected to exhibit a favorable pressure gradient, a common adage in the physics literature. In this work, we prove quantitative scattering estimates as x → ∞ 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.