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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A. E. Tzavaras, Shearing of materials exhibiting thermal softening or temperature dependent viscosity, Quart. Appl. Math. 44, 1–12 (1986)
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Article copyright:
© Copyright 1988
American Mathematical Society
