Journal Title
Title of Journal: J Evol Equ
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Abbravation: Journal of Evolution Equations
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Publisher
SP Birkhäuser Verlag Basel
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Authors: Katrin Schumacher
Publish Date: 2009/03/21
Volume: 9, Issue: 1, Pages: 1-36
Abstract
We investigate the solvability of the instationary Stokes equations with fully inhomogeneous data in Lr0THbetaq wOmega where Hbetaq wOmega is a Besselpotential space with a Muckenhoupt weight w Depending on the order of this Besselpotential space we are dealing with strong solutions or with very weak solutions Whereas in the context of lowest regularity one obtains solvability with respect to inhomogeneous data by dualization this is more delicate in the case of higher regularity where one has to introduce some additional time regularity As a preparation we introduce a generalization of the Stokes operator that is appropriate to the context of very weak solutions in weighted Besselpotential spaces
Keywords:
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