The inviscid limit of Navier-Stokes for analytic data on the half-space

Abstract

In their classical work Caflisch and Sammartino proved the inviscid limit of the incompressible Navier-Stokes equations for well-prepared data with analytic regularity in the half-space. Their proof is based on the detailed construction of Prandtl's boundary layer asymptotic expansions. In this paper, we give a direct proof of the inviscid limit for general analytic data without having to construct Prandtl's boundary layer correctors. Our analysis makes use of the boundary vorticity formulation and the abstract Cauchy-Kovalevskaya theorem on analytic boundary layer function spaces that capture unbounded vorticity.

to appear on Archive for Rational Mechanics and Analysis

References in corpus (3)

• Almost global existence for the Prandtl boundary layer equations
• Remarks on high Reynolds numbers hydrodynamics and the inviscid limit
• Sublayer of Prandtl boundary layers

Cited by in corpus (3)

• On the Euler+Prandtl expansion for the Navier-Stokes equations
• Optimal Gevrey stability of hydrostatic approximation for the Navier-Stokes equations in a thin domain
• Linear instability analysis on compressible Navier-Stokes equations with strong boundary layer