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| Bingham Flows in Periodic Domains of Infinite Length |
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Citation： |
Patrizia DONATO,Sorin MARDARE,Bogdan VERNESCU.Bingham Flows in Periodic Domains of Infinite Length[J].Chinese Annals of Mathematics B,2018,39(2):183~200 |
| Page view： 1267
Net amount： 883 |
Authors： |
Patrizia DONATO; Sorin MARDARE;Bogdan VERNESCU |
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| Abstract： |
The Bingham fluid model has been successfully used in modeling a
large class of non-Newtonian fluids. In this paper, the authors
extend to the case of Bingham fluids the results previously obtained
by Chipot and Mardare, who studied the asymptotics of the Stokes
flow in a cylindrical domain that becomes unbounded in one
direction, and prove the convergence of the solution to the
Bingham problem in a finite periodic domain, to the solution of the
Bingham problem in the infinite periodic domain, as the length of
the finite domain goes to infinity. As a consequence of this
convergence, the existence of a solution to a Bingham problem in the
infinite periodic domain is obtained, and the uniqueness of the
velocity field for this problem is also shown. Finally, they show
that the error in approximating the velocity field in the infinite
domain with the velocity in a periodic domain of length $2\ell$ has
a polynomial decay in $\ell$, unlike in the Stokes case (see
[Chipot, M. and Mardare, S., Asymptotic behaviour of the Stokes
problem in cylinders becoming unbounded in one direction, {\it
Journal de Math\'ematiques Pures et Appliqu\'ees}, {\bf 90}(2),
2008, 133--159]) where it has an exponential decay. This is in
itself an important result for the numerical simulations of
non-Newtonian flows in long tubes. |
Keywords： |
Bingham fluids, Variational inequalities |
Classification： |
35B40, 35B27, 35J87, 76D07, 74C10 |
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