Hostname: page-component-cd9895bd7-mkpzs Total loading time: 0 Render date: 2024-12-26T01:51:51.486Z Has data issue: false hasContentIssue false
  • English
  • Français

The steady state Navier–Stokes equations for incompressible flows with rotating boundaries

Published online by Cambridge University Press:  14 November 2011

Niko Sauer
Niko Sauer
Affiliation:
Faculty of Science, University of Pretoria, Pretoria 0002, South Africa
Get access Rights & Permissions [Opens in a new window]

Synopsis

When a rigid body performs a rotation in a fluid, the system of governing equations consists of conservation of linear momentum of the fluid and conservation of angular momentum of the rigid body. Since the torque at the interface involves the drag due to the fluid flow, the conservation of angular momentum may be viewed as a boundary condition for the field equations of fluid motion. The familiar no-slip condition becomes an additional equation in the system which not only governs the fluid motion, but also the motion of the rigid body. The unknown functions in the system of equations are the velocity field and the pressure field of the fluid motion and the angular velocity of the rigid body.

In this paper we obtain existence and uniqueness results for the steady state problem in which a rigid body rotates about an axis of symmetry in a viscous incompressible fluid.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 110 , Issue 1-2 , 1988 , pp. 93 - 99
Copyright
Copyright © Royal Society of Edinburgh 1988

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1Dunford, N. and Schwartz, J. T.. Linear Operators, vol. 2 (New York: Interscience, 1964).Google Scholar
2Fujita, H.. On the existence and regularity of the steady state solutions of the Navier-Stokes equation. J. Fac. Sci. Univ. Tokyo Sect. 1A Math. 9 (1961), 59–102.Google Scholar
3Hestenes, M. R.. Applications of the theory of quadratic forms in Hilbert space to the calculus of variations. Pacific J. Math. 1 (1951), 525–581.CrossRefGoogle Scholar
4Ladyzhenskaya, O. A.. The mathematical theory of viscous incompressible flow (New York: Gordon & Breach, 1963).Google Scholar
5Lions, J.-L. and Magenes, E.. Problèmes aux limites non homogènes et applications, vol. 1 (Paris: Dunod, 1968).Google Scholar
6Serrin, J.. Mathematical principles of classical fluid mechanics. Handbuch der Physik, 8/1, pp. 125–263 (Berlin: Springer, 1959).Google Scholar
7Velte, W.. Stabilitätsverhalten und Verzweigung stationärer Lösungen der Navier-Stokesschen Gleichungen. Arch. Rational Mech. Anal. 16 (1964), 97–125.CrossRefGoogle Scholar