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The motion of a fluid–rigid disc system at the zero limit of the rigid disc radius
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Dashti, Masoumeh and Robinson, James C. (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. doi:10.1007/s00205-011-0401-7 ISSN 0003-9527.
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Official URL: http://dx.doi.org/10.1007/s00205-011-0401-7
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 | ||||
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Subjects: | Q Science > QA Mathematics | ||||
Divisions: | Faculty of Science, Engineering and Medicine > 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 | ||||
Publisher: | Springer | ||||
ISSN: | 0003-9527 | ||||
Official Date: | April 2011 | ||||
Dates: |
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Volume: | Volume 200 | ||||
Number: | Number 1 | ||||
Page Range: | pp. 285-312 | ||||
DOI: | 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 (ERC) | ||||
Grant number: | EP/G007470/1 (EPSRC) |
Data sourced from Thomson Reuters' Web of Knowledge
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