Remarks on the $L^p$-approach to theStokes equation on unbounded domains
Matthias Geißert, Horst Heck, Matthias Hieber, Okihiro Sawada · Discrete and Continuous Dynamical Systems - S · 2010
Consider a domain $\Omega \subset \R^n$ with uniform $C^3$-boundary and assume that the Helmholtz projection $P$ exists on $L^p(\Omega)$ for some $ 1 < p < \infty$. Of concern are recent results on the Stokes operator in $L^p(\Omega)$ generating an analytic semigroup on $L^p(\Omega)$ and admitting maximal $L^p$-$L^q$-regularity.