Archive for Rational Mechanics and Analysis

, Volume 223, Issue 3, pp 1307–1335 | Cite as

Small Moving Rigid Body into a Viscous Incompressible Fluid

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Abstract

We consider a single disk moving under the influence of a two dimensional viscous fluid and we study the asymptotic as the size of the solid tends to zero. If the density of the solid is independent of \({\varepsilon}\), the energy equality is not sufficient to obtain a uniform estimate for the solid velocity. This will be achieved thanks to the optimal L p L q decay estimates of the semigroup associated to the fluid-rigid body system and to a fixed point argument. Next, we will deduce the convergence to the solution of the Navier–Stokes equations in \({\mathbb{R}^{2}}\).

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Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  1. 1.Univ Paris Diderot, Sorbonne Paris Cité, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586, CNRSSorbonne UniversitésParisFrance
  2. 2.Univ. Grenoble Alpes, IFGrenobleFrance
  3. 3.CNRS, IFGrenobleFrance
  4. 4.InriaVillers-lès-NancyFrance
  5. 5.Institut Élie Cartan de Lorraine,UMR 7502Vandoeuvre-lès-NancyFrance

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