2021/03/11 by Sameer Iyer, Nader Masmoudi, Iyer, Sameer +1
Engineering · Mathematics · #Analysis of PDEs (math.AP) #Computational Fluid Dynamics and Aerodynamics #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations #math.AP
paper · pdf · doi:10.48550/arxiv.2103.09170
Companion paper to arXiv:2008.12347. Accepted version in journal style
openalex publication_date 2021/03/11 · arxiv created 2021/09/09 · arxiv updated 2021/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This is the first part of a two paper sequence in which we prove the global-in-x stability of the classical Prandtl boundary layer for the 2D, stationary Navier-Stokes equations. In this part, we provide a construction of an approximate Navier-Stokes solution, obtained by a classical Euler- Prandtl asymptotic expansion. We develop here sharp decay estimates on these quantities. Of independent interest, we establish without using the classical von-Mise change of coordinates, proofs of global in x regularity of the Prandtl system. The results of this paper are used in the second part of this sequence, [IM20] (arXiv:2008.12347), to prove the asymptotic stability of the boundary layer as \eps → 0 and x → ∞.