Global Solution for the incompressible Navier-Stokes equations] { Global Solution for the incompressible Navier-Stokes equations with a class of large data in $BM{O}^{-1}({\mathbb{R}}^3)$

In this paper, we shall establish the global well-posedness, the space-time analyticity of the Navier-Stokes equations for a class of large periodic data $u_0\in BM{O}^{-1}({\mathbb{R}}^3)$. This improves the classical result of Koch & Tataru \cite{koch-tataru}, for the global well-posedness with small initial data $u_0\in BM{O}^{-1}({\mathbb{R}}^n)$.