Archive for Rational Mechanics and Analysis

, Volume 146, Issue 1, pp 59–71

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

  • B. Desjardins
  • M. J. Esteban

DOI: 10.1007/s002050050136

Cite this article as:
Desjardins, B. & Esteban, M. Arch Rational Mech Anal (1999) 146: 59. doi:10.1007/s002050050136


. 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.

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