Axially symmetric solutions to the Navier–Stokes equations in a bounded cylinder are considered. On the boundary the normal component of the velocity and the angular components of the velocity and vorticity are assumed to vanish. If the norm of the initial swirl is sufficiently small, then the regularity of axially symmetric, weak solutions is shown. The key tool is a new estimate for the stream function in certain weighted Sobolev spaces.

中文翻译：

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具有小涡流的纳维-斯托克斯方程的整体正则轴对称解

考虑有界圆柱体中纳维-斯托克斯方程的轴对称解。在边界上，速度的法向分量以及速度和涡量的角度分量被假定消失。如果初始漩涡的范数足够小，则显示轴对称弱解的规律性。关键工具是对某些加权 Sobolev 空间中的流函数的新估计。