On Stokes operators with variable viscosity in bounded and unbounded domains |
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Authors: | Helmut Abels Yutaka Terasawa |
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Institution: | (1) Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany;(2) Department of Mathematics, Hokkaido University, Kita 10, Nishi 8, Kita-Ku, Sapporo, Hokkaido 060-0810, Japan |
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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
∞
-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 -boundary for some r > d with r ≥ q, q′. In particular, the existence of an L
q
-Helmholtz projection is assumed. |
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Keywords: | Mathematics Subject Classification (2000)" target="_blank">Mathematics Subject Classification (2000) 35Q30 76D07 47A60 47F05 |
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