On the Euler + Prandtl Expansion for the Navier-Stokes Equations

Igor Kukavica, Trinh T. Nguyen, Vlad Vicol, Fei Wang

Research output: Contribution to journalArticlepeer-review

Abstract

We establish the validity of the Euler+ Prandtl approximation for solutions of the Navier-Stokes equations in the half plane with the Dirichlet boundary conditions, in the vanishing viscosity limit, for initial data which are analytic only near the boundary, and Sobolev smooth away from the boundary. Our proof does not require higher order correctors, and works directly by estimating an L1-type norm for the vorticity of the error term in the expansion Navier-Stokes- (Euler+ Prandtl). An important ingredient in the proof is the propagation of local analyticity for the Euler equation, a result of independent interest

Original languageEnglish (US)
Article number47
JournalJournal of Mathematical Fluid Mechanics
Volume24
Issue number2
DOIs
StatePublished - May 2022

Keywords

  • Analyticity
  • Euler equations
  • Inviscid limit
  • Navier-Stokes equations
  • Prandtl expansion

ASJC Scopus subject areas

  • Mathematical Physics
  • Condensed Matter Physics
  • Computational Mathematics
  • Applied Mathematics

Fingerprint

Dive into the research topics of 'On the Euler + Prandtl Expansion for the Navier-Stokes Equations'. Together they form a unique fingerprint.

Cite this