On the Stokes Resolvent Equations in Locally Uniform L p Spaces in Exterior Domains
Matthias Geißert, Yoshikazu Giga · Birkhäuser Basel eBooks · 2007
The Stokes resolvent equations are studied in locally uniform L p 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 L p spaces is that these spaces contain non-decaying functions.