Elliptic and Parabolic Equations - Abstract

Hieber, Matthias

Weak Neumann implies Stokes

In this talk we consider the Stokes and the Navier--Stokes equations on domains $OmegasubsetmathbfR^n$ with smooth but not necessarily compact boundaries. Given $1 < p < infty$, we show that the solution of the Stokes equation on these domains is goverend by an analytic semigroup $L^p_sigma(Omega)$, the Stokes semigroup, provided a suitable weak Neumann problem is uniquely solvable for these domains.
This is joint work with M. Geissert, H. Heck and O. Sawada.