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A Small Solid Body with Large Density in a Planar Fluid is Negligible

  • Jiao HeEmail author
  • Dragoş IftimieEmail author
Article
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Abstract

In this article, we consider a small rigid body moving in a viscous fluid filling the whole \(\mathbb R^2\). We assume that the diameter of the rigid body goes to 0, that the initial velocity has bounded energy and that the density of the rigid body goes to infinity. We prove that the rigid body has no influence on the limit equation by showing convergence of the solutions towards a solution of the Navier–Stokes equations in the full plane \(\mathbb {R}^{2}\).

Keywords

Incompressible flow Navier–Stokes equations Fluid–structure interaction Small obstacle Singular limit 

Notes

Acknowledgements

J.H. and D.I. have been partially funded by the ANR Project Dyficolti ANR-13-BS01-0003-01. D.I. has been partially funded by the LABEX MILYON (ANR-10-LABX-0070) of Université de Lyon, within the program “Investissements d’Avenir” (ANR-11-IDEX-0007) operated by the French National Research Agency (ANR).

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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.CNRS UMR 5208, Institut Camille JordanUniversité de Lyon, Université Lyon 1Villeurbanne CedexFrance

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