Czechoslovak Mathematical Journal

, Volume 58, Issue 4, pp 961–992

Well posedness for the system modelling the motion of a rigid body of arbitrary form in an incompressible viscous fluid

Article

DOI: 10.1007/s10587-008-0063-2

Cite this article as:
Cumsille, P. & Takahashi, T. Czech Math J (2008) 58: 961. doi:10.1007/s10587-008-0063-2

Abstract

In this paper, we consider the interaction between a rigid body and an incompressible, homogeneous, viscous fluid. This fluid-solid system is assumed to fill the whole space ℝd, d = 2 or 3. The equations for the fluid are the classical Navier-Stokes equations whereas the motion of the rigid body is governed by the standard conservation laws of linear and angular momentum. The time variation of the fluid domain (due to the motion of the rigid body) is not known a priori, so we deal with a free boundary value problem.

We improve the known results by proving a complete wellposedness result: our main result yields a local in time existence and uniqueness of strong solutions for d = 2 or 3. Moreover, we prove that the solution is global in time for d = 2 and also for d = 3 if the data are small enough.

Keywords

Navier-Stokes equations incompressible fluid rigid bodies 

Copyright information

© Mathematical Institute, Academy of Sciences of Czech Republic 2008

Authors and Affiliations

  1. 1.Departamento de Ciencias Básicas, Facultad de CienciasUniversidad del Bío-BíoChillánChile
  2. 2.Institut Elie Cartan UMR 7502, INRIANancy-Université, CNRS, Project-Team CORIDAVandœuvre-lès-Nancy, CedexFrance

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