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Communications in Mathematical Physics

, Volume 341, Issue 3, pp 1015–1065 | Cite as

On the Motion of a Small Light Body Immersed in a Two Dimensional Incompressible Perfect Fluid with Vorticity

  • Olivier Glass
  • Christophe Lacave
  • Franck Sueur
Article

Abstract

In this paper we consider the motion of a rigid body immersed in a two dimensional unbounded incompressible perfect fluid with vorticity. We prove that when the body shrinks to a massless pointwise particle with fixed circulation, the “fluid+rigid body” system converges to the vortex-wave system introduced by Marchioro and Pulvirenti (Mathematical theory of incompressible nonviscous fluids. Applied Mathematical Sciences 96, Springer-Verlag, 1994). This extends both the paper (Glass et al. Bull Soc Math France 142(3):489–536, 2014) where the case of a solid tending to a massive pointwise particle was tackled and the paper (Glass et al. Dynamics of a point vortex as limits of a shrinking solid in an irrotational fluid, 2014) where the massless case was considered but in a bounded cavity filled with an irrotational fluid.

Keywords

Vorticity Normal Form Rigid Body Laurent Series Point Vortex 
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 2015

Authors and Affiliations

  • Olivier Glass
    • 1
  • Christophe Lacave
    • 2
  • Franck Sueur
    • 3
  1. 1.CEREMADE, UMR 7534, Université Paris-Dauphine & CNRSParis Cedex 16France
  2. 2.Univ Paris Diderot, Sorbonne Paris Cité, Institut de Mathématiques de Jussieu-Paris Rive Gauche, UMR 7586, CNRS, Sorbonne Universités, UPMC Univ Paris 06ParisFrance
  3. 3.Institut de Mathématiques de Bordeaux, UMR CNRS 5251Université de BordeauxTalence CedexFrance

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