Global Mild Solutions of the Navier-Stokes Equations
  Here we establish a global well-posedness of \textit{mild} solutions to the three-dimensional incompressible Navier-Stokes equations if the initial data are in the space $\mathcal{X}^{-1}$ defined by $(1.3)$ and if the norms of the initial data in $\mathcal{X}^{-1}$ are bounded exactly by the viscosity coefficient $\mu$. 
Zhen Lei, Fang-hua Lin
math.AP