On the Stokes and Navier-Stokes equations in aperturbed half-space and an aperture domain

摘要

We discuss L~P—L~qtype estimate of the Stokes semigroup and itsapplication to the Navier-Stokes equations in a perturbed half-spaceand an aperture domain. Especially, we have the L~P-L~qtype estimateof the gradient of the Stokes semigroup for any p and q with 1 < p