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  • Cited by 2
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    This article has been cited by the following publications. This list is generated based on data provided by CrossRef.

    Carroll, Robert and Bu, Qiyue 1991. Solution of the forced nonlinear schrödinger (nls) equation using pde techniques. Applicable Analysis, Vol. 41, Issue. 1-4, p. 33.

    Grobbelaar-Van Dalsen, Maríe and Sauer, Niko 1989. Dynamic boundary conditions for the Navier–Stokes equations. Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Vol. 113, Issue. 1-2, p. 1.

  • Proceedings of the Royal Society of Edinburgh: Section A Mathematics, Volume 110, Issue 1-2
  • January 1988, pp. 93-99

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

  • Niko Sauer (a1)
  • DOI:
  • Published online: 14 November 2011

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.

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3M. R. Hestenes . Applications of the theory of quadratic forms in Hilbert space to the calculus of variations. Pacific J. Math. 1 (1951), 525581.

7W. Velte . Stabilitätsverhalten und Verzweigung stationärer Lösungen der Navier-Stokesschen Gleichungen. Arch. Rational Mech. Anal. 16 (1964), 97125.

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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
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