Almost Global Existence for the Prandtl Boundary Layer Equations

2015/02/28 by Mihaela Ignatova, Vlad Vicol · 1 citation
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Boundary (topology) #Boundary layer #Computational Fluid Dynamics and Aerodynamics #Constant (computer programming) #Euler's formula #Geodetic datum #Geometry #Mathematical analysis #Mathematics #Mechanics #Navier-Stokes equation solutions #Physics #Plane (geometry) #Prandtl number #Variable (mathematics) #math.AP

paper · pdf · doi:10.1007/s00205-015-0942-2

Fixed a number of typos

arxiv created 2015/09/25 · openalex publication_date 2015/10/15 · arxiv updated 2016/03/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We consider the Prandtl boundary layer equations on the half plane, with initial datum that lies in a weighted H¹ space with respect to the normal variable, and is real-analytic with respect to the tangential variable. The boundary trace of the horizontal Euler flow is taken to be a constant. We prove that if the Prandtl datum lies within ε of a stable profile, then the unique solution of the Cauchy problem can be extended at least up to time T_ε ≥ exp(ε^-1/ log(ε^-1)).

Citations

• A well-posedness theory for the Prandtl equations in three space variables
• Long time well-posdness of Prandtl system with small and analytic initial data
• On the inviscid limit of the Navier-Stokes equations
• Prandtl boundary layer expansions of steady Navier-Stokes flows over a moving plate

Cited by

• Sublayer of Prandtl Boundary Layers