Delve into the future of research at MiS with our preprint repository. Our scientists are making groundbreaking discoveries and sharing their latest findings before they are published. Explore repository to stay up-to-date on the newest developments and breakthroughs.
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.
