On the existence of smooth periodic solutions of 3D homogeneous Navier-Stokes equations

Abstract

In this paper, we consider the smooth solutions of 3D incompressible Navier-Stokes equations in periodic domains. We prove that, in the absence of external forces and with divergence-free smooth periodic initial data, periodic smooth solutions of the 3D Navier-Stokes equations exist for all time.

The solution for the NS equations provided can only be constant or very small magnitude