Weighted L p -estimates for Stokes flow in ℝ + n with applications to the non-stationary Navier-Stokes flow

Abstract

We study the time-decay properties of weighted norms of solutions to the Stokes equations and the Navier-Stokes equations in the half-space ℝ+n (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.