Note on an example of a zero viscosity limit for Navier-Stokes flows with the initial boundary layer in the disk

Abstract

In this Letter, we give an example of Navier-Stokes flow with a viscosityv, which converges to Euler flow inL 2 norm asv → 0. Our Navier-Stokes flow has a discontinuity on the boundary at the initial time, the so-called ‘initial layer’, and its initial data has singularity asymptotically asv → 0 near the boundary. Even with these singularities, it can be said that our Navier-Stoke flow can converge to some Euler flow inL 2 norm.