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The motion of a fluid-rigid disc system at the zero limit of the rigid disc radius

journal contribution
posted on 2023-06-08, 12:45 authored by Masoumeh DashtiMasoumeh Dashti, James Robinson
We consider the two-dimensional motion of the coupled system of a viscous incompressible fluid and a rigid disc moving with the fluid, in the whole plane. The fluid motion is described by the Navier-Stokes equations and the motion of the rigid body by conservation laws of linear and angular momentum. We show that, assuming that the rigid disc is not allowed to rotate, as the radius of the disc goes to zero, the solution of this system converges, in an appropriate sense, to the solution of the Navier-Stokes equations describing the motion of only fluid in the whole plane. We also prove that the trajectory of the centre of the disc, at the zero limit of its radius, coincides with a fluid particle trajectory.

History

Publication status

  • Published

Journal

Archive for Rational Mechanics and Analysis

ISSN

0003-9527

Publisher

Springer Verlag

Issue

1

Volume

200

Page range

285-312

Department affiliated with

  • Mathematics Publications

Full text available

  • No

Peer reviewed?

  • Yes

Legacy Posted Date

2012-11-05

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