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$ L^{p}$-theory for strong solutions to fluid-rigid body interaction in Newtonian and generalized Newtonian fluids


Authors: Matthias Geissert, Karoline Götze and Matthias Hieber
Journal: Trans. Amer. Math. Soc. 365 (2013), 1393-1439
MSC (2010): Primary 35Q30; Secondary 76A05, 76D03, 74F10
DOI: https://doi.org/10.1090/S0002-9947-2012-05652-2
Published electronically: August 3, 2012
MathSciNet review: 3003269
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Abstract: Consider the system of equations describing the motion of a rigid body immersed in a viscous, incompressible fluid of Newtonian or generalized Newtonian type. The class of fluids considered includes in particular shear-thinning or shear-thickening fluids of power-law type of exponent $ d\geq 1$. We develop a method to prove that this system admits a unique, local, strong solution in the $ L^p$-setting. The approach presented in the case of generalized Newtonian fluids is based on the theory of quasi-linear evolution equations and requires that the exponent $ p$ satisfies the condition $ p>5$.


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Additional Information

Matthias Geissert
Affiliation: Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany
Email: geissert@mathematik.tu-darmstadt.de

Karoline Götze
Affiliation: IRTG 1529: Mathematical Fluid Dynamics, Technische Universität Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany
Address at time of publication: Weierstrass Institute, Mohrenstrasse 39, 10117 Berlin, Germany
Email: goetze@mathematik.tu-darmstadt.de, karoline.goetze@wias-berlin.de

Matthias Hieber
Affiliation: Fachbereich Mathematik, Technische Universität Darmstadt, Schlossgartenstr. 7, 64289 Darmstadt, Germany
Email: hieber@mathematik.tu-darmstadt.de

DOI: https://doi.org/10.1090/S0002-9947-2012-05652-2
Keywords: Fluid-rigid body interaction, strong $L^{p}$-solutions, generalized Newtonian fluids
Received by editor(s): September 27, 2010
Received by editor(s) in revised form: May 17, 2011, and June 14, 2011
Published electronically: August 3, 2012
Article copyright: © Copyright 2012 American Mathematical Society

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