Global Mild Solutions of the Navier-Stokes Equations

Abstract

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 $\mu$.