Skip to main content
×
Home
    • Aa
    • Aa

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

  • Niko Sauer (a1)
Synopsis
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.

Copyright
References
Hide All
1Dunford N. and Schwartz J. T.. Linear Operators, vol. 2 (New York: Interscience, 1964).
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), 59102.
3Hestenes M. R.. Applications of the theory of quadratic forms in Hilbert space to the calculus of variations. Pacific J. Math. 1 (1951), 525581.
4Ladyzhenskaya O. A.. The mathematical theory of viscous incompressible flow (New York: Gordon & Breach, 1963).
5Lions J.-L. and Magenes E.. Problèmes aux limites non homogènes et applications, vol. 1 (Paris: Dunod, 1968).
6Serrin J.. Mathematical principles of classical fluid mechanics. Handbuch der Physik, 8/1, pp. 125263 (Berlin: Springer, 1959).
7Velte W.. Stabilitätsverhalten und Verzweigung stationärer Lösungen der Navier-Stokesschen Gleichungen. Arch. Rational Mech. Anal. 16 (1964), 97125.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Proceedings of the Royal Society of Edinburgh Section A: Mathematics
  • ISSN: 0308-2105
  • EISSN: 1473-7124
  • URL: /core/journals/proceedings-of-the-royal-society-of-edinburgh-section-a-mathematics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 9 *
Loading metrics...

Abstract views

Total abstract views: 117 *
Loading metrics...

* Views captured on Cambridge Core between September 2016 - 24th October 2017. This data will be updated every 24 hours.