The motion of a fluid–rigid disc system at the zero limit of the rigid disc radius
Dashti, Masoumeh and Robinson, James C. (James Cooper), 1969-. (2011) The motion of a fluid–rigid disc system at the zero limit of the rigid disc radius. Archive for Rational Mechanics and Analysis, Volume 200 (Number 1). pp. 285-312. ISSN 0003-9527Full text not available from this repository.
Official URL: http://dx.doi.org/10.1007/s00205-011-0401-7
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.
|Item Type:||Journal Article|
|Subjects:||Q Science > QA Mathematics|
|Divisions:||Faculty of Science > Mathematics|
|Library of Congress Subject Headings (LCSH):||Navier–Stokes equations, Viscous flow, Dynamics, Rigid|
|Journal or Publication Title:||Archive for Rational Mechanics and Analysis|
|Official Date:||April 2011|
|Page Range:||pp. 285-312|
|Access rights to Published version:||Restricted or Subscription Access|
|Funder:||Warwick Postgraduate Research Fellowship , Engineering and Physical Sciences Research Council (EPSRC), European Research Council (ERC)|
|Grant number:||EP/G007470/1 (EPSRC)|
1. Adams, R.A.: Sobolev Spaces. Academic Press, New York, 1975
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