Global Well-Posedness for Navier-Stokes Equations with Small Initial Value in B-n,infinity(0) (Omega)

We prove global well-posedness for instationary Navier-Stokes equations with initial data in Besov space in whole and half space, and bounded domains of , . To this end, we prove maximal -regularity of the sectorial operators in some Banach spaces and, in particular, maximal -regularity of the Stokes operator in little Nikolskii spaces , , which are of independent significance. Then, based on the maximal regularity results and estimates of the Stokes semigroups, we prove global well-posedness for Navier-Stokes equations under smallness condition on via a fixed point argument using Banach fixed point theorem.CAS-TWAS Postdoctoral Fellowship [3240267229]SCI(E)EIARTICLEmath.inst@star-co.net.kp1103-1311