On Stokes operators with variable viscosity in bounded and unbounded domains

We consider a generalization of the Stokes resolvent equation, where the constant viscosity is replaced by a general given positive function. Such a system arises in many situations as linearized system, when the viscosity of an incompressible, viscous fluid depends on some other quantities. We prove that an associated Stokes-like operator generates an analytic semi-group and admits a bounded H-infinity-calculus, which implies the maximal L-q-regularity of the corresponding parabolic evolution equation. The analysis is done for a large class of unbounded domains with W-r(2-1/r)-boundary for some r > d with r >= q, q'. In particular, the existence of an L-q-Helmholtz projection is assumed.