A note on the vanishing viscosity limit in the Yudovich class

Abstract

We 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 ${\left(\nu /|\log \nu |\right)}^{\frac{1}{2}\exp (-Ct)}$ bound, which slightly improves upon earlier results by Chemin.

Accepted version

Cited by in corpus (5)

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• On the vanishing viscosity limit for 2D incompressible flows with unbounded vorticity
• On the dynamics of point vortices for the 2D Euler equation with $L^p$ vorticity
• Propagation of logarithmic regularity and inviscid limit for the 2D Euler equations
• On Maximum Enstrophy Dissipation in 2D Navier-Stokes Flows in the Limit of Vanishing Viscosity