Global mild solutions of Navier‐Stokes equations

We establish a global well‐posedness of mild solutions to the three‐dimensional, incompressible Navier‐Stokes equations if the initial data are in the space X⁻¹ defined by amssym X‐1 = ∈ D⁽R³): ∫_R³|ξ|‐1|f|dξ < ∞\ and if the norms of the initial data in X⁻¹ are bounded exactly by the viscosity coefficient μ.