Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



Stabilization of adiabatic rigid body rotation by dissipation

Author: M. A. Boudourides
Journal: Quart. Appl. Math. 46 (1988), 49-54
MSC: Primary 76U05
DOI: https://doi.org/10.1090/qam/934680
MathSciNet review: 934680
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Abstract: We consider the adiabatic tangential flow of an incompressible Newtonian fluid with temperature-dependent viscosity between two coaxial cylinders, one of which is rotating, while the other is kept stress-free. We show that every classical solution approaches, as time goes to infinity, a uniform rigid body rotation at fixed temperature, thus establishing the stabilizing role of dissipation. The proof is based on a priori estimates, obtained with the help of certain identities for solutions of the governing equations.

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DOI: https://doi.org/10.1090/qam/934680
Article copyright: © Copyright 1988 American Mathematical Society

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