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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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$L^{p}$-theory for strong solutions to fluid-rigid body interaction in Newtonian and generalized Newtonian fluids
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by Matthias Geissert, Karoline Götze and Matthias Hieber PDF
Trans. Amer. Math. Soc. 365 (2013), 1393-1439 Request permission

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
  • MR Author ID: 270487
  • Email: hieber@mathematik.tu-darmstadt.de
  • 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
  • © Copyright 2012 American Mathematical Society
  • 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
  • MathSciNet review: 3003269