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We have decided to discontinue the publication of preprints on our preprint server as of 1 March 2024. The publication culture within mathematics has changed so much due to the rise of repositories such as ArXiV (www.arxiv.org) that we are encouraging all institute members to make their preprints available there. An institute's repository in its previous form is, therefore, unnecessary. The preprints published to date will remain available here, but we will not add any new preprints here.

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.

Received:
Mar 25, 2008
Published:
Mar 26, 2008
MSC Codes:
35Q30, 76D07, 47A60, 47F05
Keywords:
Stokes operator, Stokes equation, unbounded domains, bounded imaginary powers, $H_\infty$-calculus

Related publications

inJournal
2009 Journal Open Access
Helmut Abels and Yutaka Terasawa

On Stokes operators with variable viscosity in bounded and unbounded domains

In: Mathematische Annalen, 344 (2009) 2, pp. 381-429