Global mild solutions of Navier‐Stokes equations

Abstract 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 = \f {D^ (R³): ₑ³||^‐1|f|d < \} and if the norms of the initial data in X^-1 are bounded exactly by the viscosity coefficient μ. © 2010 Wiley Periodicals, Inc.