Abstract
AbstractWe consider the inviscid limit for the two-dimensional Navier–Stokes equations in the class of integrable and bounded vorticity fields. It is expected that the difference between the Navier–Stokes and Euler velocity fields vanishes in $L^2$ with an order proportional to the square root of the viscosity constant $\nu $. Here, we provide an order $ (\nu /|\log \nu | )^{\frac 12\exp (-Ct)}$ bound, which slightly improves upon earlier results by Chemin.
Highlights
1 Introduction e convergence of solutions of the Navier–Stokes equations towards solutions of the Euler equations in the limit of vanishing viscosity has been an ongoing research topic for many years
We study the inviscid limit for integrable and bounded vorticity fields
We are interested in the rate of L convergence of the Navier– Stokes velocity fields towards the Euler velocity fields
Summary
1 Introduction e convergence of solutions of the Navier–Stokes equations towards solutions of the Euler equations in the limit of vanishing viscosity has been an ongoing research topic for many years. We will work on the Navier–Stokes and Euler equations in vorticity formulations. E (scalar) vorticity fields are computed as the rotations of the velocity vectors and are denoted by ων in the case of the Navier–Stokes and ω in the case of the Euler equations.
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