2017/05/12 by Emmanuel Grenier, Toan T. Nguyen
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Blasius boundary layer #Boundary (topology) #Boundary layer #Boundary layer thickness #Classical mechanics #Convection #Flow separation #Instability #Inviscid flow #Laminar sublayer #Limit (mathematics) #Mathematical analysis #Mathematics #Mechanics #Navier-Stokes equation solutions #No-slip condition #Nonlinear Partial Differential Equations #Physics #Prandtl number #Reynolds number #Turbulence #Turbulent Prandtl number #math.AP
paper · pdf · doi:10.1007/s00205-018-1235-3
arxiv created 2017/05/12 · openalex publication_date 2018/03/02 · arxiv updated 2018/04/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/06
The aim of this paper is to investigate the stability of Prandtl boundary layers in the vanishing viscosity limit: ν→ 0. In \citeGrenier, one of the authors proved that there exists no asymptotic expansion involving one Prandtl's boundary layer with thickness of order √ν, which describes the inviscid limit of Navier-Stokes equations. The instability gives rise to a viscous boundary sublayer whose thickness is of order ν3/4. In this paper, we point out how the stability of the classical Prandtl's layer is linked to the stability of this sublayer. In particular, we prove that the two layers cannot both be nonlinearly stable in L^∞. That is, either the Prandtl's layer or the boundary sublayer is nonlinearly unstable in the sup norm.