Quarterly of Applied Mathematics Quarterly of Applied Mathematics
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Existence of turning points for the response diagram of the Poiseuille flow with prescribed flow-rate

Author(s): Giovanni Cimatti
Journal: Quart. Appl. Math. 65 (2007), 523-528.
MSC (2000): Primary 76D03, 76D05
Posted: June 6, 2007
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Abstract: We study the stationary Poiseuille flow in a cylindrical channel of arbitrary cross-section with temperature dependent viscosity and internal dissipation. We assume the flow-rate $ \Phi$ given and the axial pressure gradient $ \mu$ unknown. This leads to a non-local problem. We show the existence in the response diagram, the plane $ (\Phi,\mu)$, of two turning points.

References:

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H. Beirão Da Veiga, Time-Periodic Solutions of the Navier-Stokes Equations inUnbounded Cylindrical Domains - Leray's Problem for Periodic Flow, Arch. Rational Mech. Anal. 178 (2005) 301-325. MR 2196495 (2006k:35209)

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G. P. Galdi and A. M. Robertson, The Relation Between Flow Rate and Axial Pressure Gradient for Time-Periodic Poiseuille Flow in a Pipe, J. Math. Fluid. Mech. 7 (2005) 215-223. MR 2192849 (2006j:76038)

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G. P. Galdi, An Introduction to the Mathematical Theory of the Navier-Stokes Equations: Linearized Steady Problems, Revised Edition, Springer Tracts in Natural Philosophy, Vol. 38, Springer-Verlag, New York, 1998. MR 1284205 (95i:35216a)

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G. Cimatti, The Poiseuille Solution with Temperature Dependent Viscosity, Applicable Analysis, Vol. 84 (2005) 451-461. MR 2151274 (2006a:35247)

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Additional Information:

Giovanni Cimatti
Affiliation: Dipartimento di Matematica, Largo Bruno Pontecorvo 5, Pisa, Italy
Email: cimatti@dm.unipi.it

PII: S0033-569X-07-01058-1
Keywords: Poiseuille flow, temperature dependent viscosity, existence and uniqueness of solutions.
Received by editor(s): September 28, 2006
Posted: June 6, 2007
Copyright of article: Copyright 2007, Brown University
The copyright for this article reverts to public domain after 28 years from publication.


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