Hokkaido University Preprint Series in Mathematics
The Stokes resolvent equations are studied in locally uniform Lp spaces where the domain is an exterior of a bounded domain. The unique existence of a solution of the Stokes resolvent equations is proved with a resolvent estimate. In particular, the analyticity of the Stokes semigroup is established. An interesting aspect of locally uniform Lp spaces is that these spaces contain non-decaying functions.