  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
$u_0 \in BMO^{-1}(\mathbb{R}^3)$. This improves the classical result of Koch \&
Tataru \cite{koch-tataru}, for the global well-posedness with small initial
data $u_0 \in BMO^{-1}(\mathbb{R}^n)$.
