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MiS Preprint
25/2008
On Stokes Operators with Variable Viscosity in Bounded and Unbounded Domains
Helmut Abels and Yutaka Terasawa
Abstract
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 $H_\infty$-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 $W^{2-\frac1r}_r$-boundary for some $r>d$ with $r\geq q$. In particular, the existence of an $L^q$-Helmholtz projection is assumed.
