The regularity of 2D Navier–Stokes flow is well known. In this article we study the relationship of 3D and 2D flow, and the regularity of the 3D Naiver–Stokes equations with viewpoint of 2D equations. We consider the problem in the Cartesian and in the cylindrical coordinates.
The author was supported under the framework of international cooperation program managed by the National Research Foundation of Korea (NRF) (NRF-2016K2A9A2A06005080), and by the Basic Science Research Program funded by the NRF, Ministry of Education, Science and Technology (NRF-2015R1D1A1A01057976).
