Strong solutions to the Stokes equations of a flow around a rotating body in weighted Lq spaces |
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Authors: | Šárka Nečasová Katrin Schumacher |
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Institution: | 1. Mathematical Institute of the Academy of Sciences of the Czech Republic, ?itná 25, 115 67 Praha 1, Czech Republic;2. Department of Mathematics, Technische Universit?t Darmstadt, 64289 Darmstadt, Germany |
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Abstract: | We consider the motion of a fluid in the exterior of a rotating obstacle. This leads to a modified version of the Stokes system which we consider in the whole space ${\mathds R}^n$, n = 2 or n = 3 and in an exterior domain $D\subset {\mathds R}^3$. For every q ∈ (1, ∞) we prove existence of solutions and estimates in function spaces with weights taken from a subclass of the Muckenhoupt class Aq. Moreover, uniqueness is shown modulo a vector space of dimension 3. © 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim |
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Keywords: | Strong solution Stokes problem weighted spaces exterior domain nonhomogeneous case existence uniqueness MSC (2010) Primary: 76D05 35Q30 Secondary: 42B25 46E35 |
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