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arXiv · 1912.07345

A note on the vanishing viscosity limit in the Yudovich class

Christian Seis
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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 $\left(\nu/|\log\nu|\right)^{\frac12\exp(-Ct)}$ bound, which slightly improves upon earlier results by Chemin.

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Christian Seis. 2019-12-16. A note on the vanishing viscosity limit in the Yudovich class. https://doi.org/10.4153/s0008439520000296

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