Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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On the higher-order boundary conditions for incompressible nonlinear bipolar fluid flow


Authors: Hamid Bellout and Frederick Bloom
Journal: Quart. Appl. Math. 71 (2013), 773-785
MSC (2010): Primary 76A05, 35K52
DOI: https://doi.org/10.1090/S0033-569X-2013-01330-9
Published electronically: September 4, 2013
MathSciNet review: 3136995
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Abstract | References | Similar Articles | Additional Information

Abstract: The higher-order boundary conditions associated with the flow of an incompressible, nonlinear, bipolar viscous fluid in a bounded domain are derived; these boundary conditions differ from the various ad hoc sets of higher-order boundary conditions that have been used in work involving fluid dynamics models employing higher-order gradients of the velocity field. The derivation presented is based on a principle of virtual work and some deep results of Heron on higher-order traces of divergence-free vector fields.


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Additional Information

Hamid Bellout
Affiliation: Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115
Email: bellout@math.niu.edu

Frederick Bloom
Affiliation: Department of Mathematical Sciences, Northern Illinois University, DeKalb, Illinois 60115
Email: bloom@math.niu.edu

DOI: https://doi.org/10.1090/S0033-569X-2013-01330-9
Keywords: Incompressible, bipolar fluid, higher-order boundary conditions, virtual work
Received by editor(s): February 22, 2012
Received by editor(s) in revised form: April 20, 2012
Published electronically: September 4, 2013
Article copyright: © Copyright 2013 Brown University
The copyright for this article reverts to public domain 28 years after publication.

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