We study the time-decay properties of weighted norms of solutions to the Stokes equations and the Navier-Stokes equations in the half-space Rn+ (n 2). Three kinds of the weighted Lp-Lr estimates are established for the Stokes semigroup generated by the Stokes operator in the half-space R+n (n 2). As an application of the weighted estimates of the Stokes semigroup, a class of local and global strong solutions in weighted Lp (R+n) are constructed, following the approach given by Kato.
HE Cheng1 & WANG LiZhen21Division of Mathematics, Department of Mathematical and Physical Sciences, National Natural Science Foundation of China, Beijing 100085, China
