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Stopping a Viscous Fluid by a Feedback Dissipative Field: Thermal Effects without Phase Changing

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Antontsev, S.N. and Díaz Díaz, Jesús Ildefonso and Oliveira, H.B. de (2005) Stopping a Viscous Fluid by a Feedback Dissipative Field: Thermal Effects without Phase Changing. In Trends in Partial Differential Equations of Mathematical Physics. Progress in Nonlinear Differential Equations and Their Applications (61). Birkhäuser, Basel, pp. 1-14. ISBN 3-7643-7165-X

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Abstract

We show how the action on two simultaneous effects (a suitable coupling about velocity and temperature and a low range of temperature but upper that the phase changing one) may be responsible of stopping a viscous fluid without any changing phase. Our model involves a system, on an unbounded pipe, given by the planar stationary Navier-Stokes equation perturbed with a sublinear term f(x, θ, u) coupled with a stationary (and possibly nonlinear) advection diffusion equation for the temperature θ.After proving some results on the existence and uniqueness of weak solutions we apply an energy method to show that the velocity u vanishes for x large enough.


Item Type:Book Section
Uncontrolled Keywords:Non-Newtonian fluids; nonlinear thermal diffusion equations; feedback dissipative field; energy method; heat and mass transfer;localization effect.
Subjects:Sciences > Physics
ID Code:30728
Deposited On:10 Jun 2015 10:34
Last Modified:12 Dec 2018 15:07

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