We study the vanishing viscosity limit for the three-dimensional incompressible Navier–Stokes equations in terms of the relative vorticity in the setting of axisymmetric velocity fields without swirl. We show that the weak convergence of relative vorticity to a renormalized solution of the Euler equations, established by Nobili and Seis, can be upgraded to strong convergence.

中文翻译：

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关于无旋流的 3D 轴对称流的消失粘度极限

我们根据无旋流的轴对称速度场设置中的相对涡度研究了三维不可压缩纳维-斯托克斯方程的消失粘度极限。我们证明，相对涡度对由 Nobili 和 Seis 建立的欧拉方程重整化解的弱收敛可以升级为强收敛。