Global regularity criterion for the 3D Navier-Stokes equations with large data

Abstract

In this paper, we study the global regularity of strong solution to the Cauchy problem of 3D incompressible Navier-Stokes equations with large data and non-zero force. We prove that the strong solution exists globally for $\nabla u\in L^{\alpha }\left(0,T,L^2\left(\Omega \right)\right)$ with $2\le \alpha \le 4$.

04 pages