Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



On the derivation of boundary conditions from the global principles of continuum mechanics

Author: Gerald G. Kleinstein
Journal: Quart. Appl. Math. 63 (2005), 469-478
MSC (2000): Primary 76A02; Secondary 74A15
DOI: https://doi.org/10.1090/S0033-569X-05-00966-1
Published electronically: April 11, 2005
MathSciNet review: 2169029
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Abstract: We consider the motion of a fluid exterior to a moving rigid obstacle, or interior to a moving rigid shell. The boundary conditions, such as the no-slip condition and the condition of an isothermal wall, applied in the solution of the system of differential equations describing these motions, are currently assumed to be an approximation derived from experimental observation rather than an exact law. It is the purpose of this paper to show that the boundary conditions at a material interface between a fluid and a solid are derivable from the global principles of balance of continuum mechanics and the Clausius-Duhem inequality.

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Additional Information

Gerald G. Kleinstein
Affiliation: 10 Emerson Place, Boston MA 02114
Email: ggkleinstein@rcn.com

DOI: https://doi.org/10.1090/S0033-569X-05-00966-1
Keywords: Navier-Stokes equations, boundary conditions, entropy condition
Received by editor(s): June 30, 2004
Published electronically: April 11, 2005
Article copyright: © Copyright 2005 Brown University

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