Archive for Rational Mechanics and Analysis

, Volume 161, Issue 2, pp 113–147 | Cite as

Global Weak Solutions¶for the Two-Dimensional Motion¶of Several Rigid Bodies¶in an Incompressible Viscous Fluid

  • Jorge Alonso San Martín
  • Victor Starovoitov
  • Marius Tucsnak


We consider the two-dimensional motion of several non-homogeneous rigid bodies immersed in an incompressible non-homogeneous viscous fluid. The fluid, and the rigid bodies are contained in a fixed open bounded set of ℝ2. The motion of the fluid is governed by the Navier-Stokes equations for incompressible fluids and the standard conservation laws of linear and angular momentum rule the dynamics of the rigid bodies. The time variation of the fluid domain (due to the motion of the rigid bodies) is not known a priori, so we deal with a free boundary value problem. The main novelty here is thedemonstration of the global existence of weak solutions for this problem. More precisely, the global character of the solutions we obtain is due to the fact that we do not need any assumption concerning the lack of collisions between several rigid bodies or between a rigid body and the boundary. We give estimates of the velocity of the bodies when their mutual distance or the distance to the boundary tends to zero.


Angular Momentum Time Variation Weak Solution Rigid Body Free Boundary 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Jorge Alonso San Martín
    • 1
  • Victor Starovoitov
    • 2
  • Marius Tucsnak
    • 3
  1. 1.Departamento de Ingeniería Matemática¶Centro de Modelamiento Matemático¶Universidad de Chile¶Casilla 170/3 - Correo 3, Santiago, Chile¶e-mail: jorge@dim.uchile.clCL
  2. 2.Lavrentyev Institute of Hydrodynamics¶Novosibirsk 630090, Russia¶e-mail: star@hydro.nsc.ruRU
  3. 3.Institut Elie Cartan, Faculté des Sciences, BP239¶54506 Vandoeuvre-les-Nancy, Cedex, France¶e-mail:¶and INRIA Lorraine, Projet CORIDAFR

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