The paper considers the regularity problem on three-dimensional incompressible Navier-Stokes equations in general orthogonal curvilinear coordinate systems. We establish one regularity criteria of the weak solutions involving only in a vorticity component and one a priori estimate on the solution that is bounded for to three-dimensional incompressible Navier-Stokes equations in orthogonal curvilinear coordinate systems. These extent greatly the corresponding results on axisymmetric cylindrical flow.

中文翻译：

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正交曲线坐标系中3D不可压缩Navier-Stokes方程的正则性准则和先验估计

本文考虑了一般正交曲线坐标系中三维不可压缩Navier-Stokes方程的正则性问题。我们只建立在涡组件涉及弱解的一个规律性的标准，一个在解决先验估计是有界的正交曲线坐标系中的三维不可压缩Navier-Stokes方程。这些程度极大地增加了轴对称圆柱流的相应结果。