We prove that given initial data , forcing and any T > 0, the solutions u^ν of Navier-Stokes converge strongly in for any p ∈ [1, ∞) to the unique Yudovich weak solution u of the Euler equations. A consequence is that vorticity distribution functions converge to their inviscid counterparts. As a by-product of the proof, we establish continuity of the Euler solution map for Yudovich solutions in the L^p vorticity topology. The main tool in these proofs is a uniformly controlled loss of regularity property of the linear transport by Yudovich solutions. Our results provide a partial foundation for the Miller-Robert statistical equilibrium theory of vortices as it applies to slightly viscous fluids. © 2020 Wiley Periodicals LLC.

中文翻译：

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Yudovich 类涡度分布的无粘性极限

我们证明，给定初始数据，强迫和任何T  > 0，Navier-Stokes的解u ^ν强烈收敛于任何p  ∈ [1, ∞) 到欧拉方程的唯一 Yudovich 弱解u。结果是涡度分布函数收敛到它们的无粘性对应物。作为证明的副产品，我们建立了L ^{p 中}Yudovich 解的欧拉解图的连续性涡度拓扑。这些证明中的主要工具是由 Yudovich 解决方案统一控制的线性传输的规律性损失。我们的结果为适用于微粘性流体的 Miller-Robert 涡旋统计平衡理论提供了部分基础。© 2020 威利期刊有限责任公司。