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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关于 Yudovich 级中消失粘度极限的说明

我们考虑可积和有界涡量场类中二维 Navier-Stokes 方程的无粘极限。预计纳维-斯托克斯和欧拉速度场之间的差异在 $L^2$ 中消失，其阶数与粘度常数 $\nu$ 的平方根成正比。在这里，我们提供了一个订单 $\left(\nu/|\log\nu|\right)^{\frac12\exp(-Ct)}$ 边界，它比 Chemin 的早期结果略有改进。