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Archive for Rational Mechanics and Analysis

, Volume 146, Issue 1, pp 59–71 | Cite as

Existence of Weak Solutions for the Motion of Rigid Bodies in a Viscous Fluid

  • B. Desjardins
  • M. J. Esteban
Article

Abstract

. We study the evolution of a finite number of rigid bodies within a viscous incompressible fluid in a bounded domain of \(\R^d$ $(d=2$ or $3)\) with Dirichlet boundary conditions. By introducing an appropriate weak formulation for the complete problem, we prove existence of solutions for initial velocities in \(H^1_0(\Omega)\). In the absence of collisions, solutions exist for all time in dimension 2, whereas in dimension 3 the lifespan of solutions is infinite only for small enough data.

Keywords

Boundary Condition Weak Solution Rigid Body Finite Number Bounded Domain 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 1999

Authors and Affiliations

  • B. Desjardins
    • 1
  • M. J. Esteban
    • 2
  1. 1.Département de Mathématiques et d'Informatique, Ecole Normale Supérieure, 45 rue d'Ulm, 75005 Paris, France e‐mail: desjardi@dmi.ens.frFR
  2. 2.CEREMADE (UMR 7534), Université Paris‐Dauphine, Place de Lattre de Tassigny, 75775 Paris Cedex 16, e‐mail: esteban@ceremade.dauphine.frFR

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