Y.: On Stokes operators with variable viscosity in bounded and unbounded

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∞-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 2 − 1 r r-boundary for some r> d with r ≥ q. In particular, the existence of an Lq-Helmholtz projection is assumed