Analysis Seminar

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

Speaker: Christophe Lacave, Institut de mathématiques de Jussieu

Location: Warren Weaver Hall 1302

Date: Thursday, October 10, 2013, 11 a.m.

Synopsis:

In this talk, we consider the motion of a small solid body in a planar ideal fluid, and the limit behavior of the system as the solid body shrinks to a point. We study two regimes:

• in the case of a fixed mass, we prove that the solutions converge to a variant of the vortex-wave system where the vortex, placed in the point occupied by the shrunk body, is accelerated by a lift force similar to the Kutta-Joukowski force of the irrotational theory.
• in the case of a fixed density, the limit behavior is exactly the vortex-wave system.

This work is in collaboration with O. Glass (Paris Dauphine) and F. Sueur (Paris 6-UPMC).