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, Vol.200 (No.1). pp. 285-312. ISSN 0003-9527

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Abstract

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
Journal or Publication Title:	Archive for Rational Mechanics and Analysis
Publisher:	Springer
ISSN:	0003-9527
Date:	April 2011
Volume:	Vol.200
Number:	No.1
Page Range:	pp. 285-312
Identification Number:	10.1007/s00205-011-0401-7
Status:	Peer Reviewed
Publication Status:	Published
Access rights to Published version:	Restricted or Subscription Access
Funder:	Warwick Postgraduate Research Fellowship , Engineering and Physical Sciences Research Council (EPSRC), European Research Council
Grant number:	EPSRC (EP/G007470/1)
URI:	http://wrap.warwick.ac.uk/id/eprint/41417

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