We show strong convergence of the vorticities in the vanishing viscosity limit for the incompressible Navier–Stokes equations on the two-dimensional torus, assuming only that the initial vorticity of the limiting Euler equations is in L ^p for some p > 1. This substantially extends a recent result of Constantin, Drivas and Elgindi, who proved strong convergence in the case p = ∞. Our proof, which relies on the classical renormalisation theory of DiPerna–Lions, is surprisingly simple.

中文翻译：

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关于具有无界涡度的二维不可压缩流动的粘度消失极限

我们在二维环面上的不可压缩 Navier-Stokes 方程的消失粘度极限中显示了涡度的强收敛，仅假设限制 Euler 方程的初始涡度在某些p > 1 的L ^p中。这大大扩展Constantin、Drivas 和 Elgindi 的最新结果，他们证明了在p = ∞的情况下强收敛。我们的证明依赖于 DiPerna-Lions 的经典重整化理论，非常简单。