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The Bingham flow in periodic domains Mardare, Sorin
Description
We consider a Bingham flow in a domain which is periodic in one direction and we are interested in the asymptotic behaviour of the solution to the stationary Bingham problem as the length 2l of the domain (in the periodic direction) goes to infinity. In order to do that we follow the methods used in [CM], where the same study has been done for the Stokes system. However, the techniques in [CM] need some important adaptations in order to treat the difficulties related to the nonlinearity of the problem. Our main result states that the velocity of the fluid converges strongly in the H1-norm to the solution of a Bingham problem in the infinite periodic domain. Nevertheless, the speed of the convergence is much lower than the one obtained for the (linear) Stokes problem. More specifically, for a Bingham fluid, the rate of convergence is of the order of l^−a with 0 < a < 1/2, while being exponential for the Stokes problem, 2 i.e. of the order of e^−αl for some positive α. This is a joint work with Patrizia Donato and Bogdan Vernescu.
Item Metadata
Title |
The Bingham flow in periodic domains
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Creator | |
Publisher |
Banff International Research Station for Mathematical Innovation and Discovery
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Date Issued |
2015-09-03T09:47
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Description |
We consider a Bingham flow in a domain which is periodic in one direction and we are interested in the asymptotic behaviour of the solution to the stationary Bingham problem as the length 2l of the domain (in the periodic direction) goes to infinity. In order to do that we follow the methods used in [CM], where the same study has been done for the Stokes system. However, the techniques in [CM] need some important adaptations in order to treat the difficulties related to the nonlinearity of the problem.
Our main result states that the velocity of the fluid converges strongly
in the H1-norm to the solution of a Bingham problem in the infinite
periodic domain. Nevertheless, the speed of the convergence is much
lower than the one obtained for the (linear) Stokes problem. More
specifically, for a Bingham fluid, the rate of convergence is of the order
of l^−a with 0 < a < 1/2, while being exponential for the Stokes problem, 2
i.e. of the order of e^−αl for some positive α.
This is a joint work with Patrizia Donato and Bogdan Vernescu.
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Extent |
50 minutes
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Subject | |
Type | |
File Format |
video/mp4
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Language |
eng
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Notes |
Author affiliation: Universite de Rouen
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Series | |
Date Available |
2016-03-11
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Provider |
Vancouver : University of British Columbia Library
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Rights |
Attribution-NonCommercial-NoDerivatives 4.0 International
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DOI |
10.14288/1.0228167
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URI | |
Affiliation | |
Peer Review Status |
Unreviewed
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Scholarly Level |
Faculty
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Rights URI | |
Aggregated Source Repository |
DSpace
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Item Media
Item Citations and Data
Rights
Attribution-NonCommercial-NoDerivatives 4.0 International