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

Author(s): Gerald G. Kleinstein
Journal: Quart. Appl. Math. 63 (2005), 469-478.
MSC (2000): Primary 76A02; Secondary 74A15
Posted: April 11, 2005
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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.

References:

1.
Batchelor, G. K., An Introduction to Fluid Dynamics, Cambridge University Press, 1967. MR 1744638 (2000j:76001)

2.
Gurtin, M. E., An Introduction to Continuum Mechanics, Academic Press, 1981. MR 0636255 (84c:73001)

3.
Keller, J. B., Geometrical acoustics I. The theory of weak shock waves, J. Appl. Physics, 1954, 25, 938-947. MR 0067654 (16,761e)

4.
Kleinstein, G. G., On the non-persistence of irrotational motion in a viscous heat-conducting fluid, Arch. Ratl. Mech. Anal., 1988, 101 (No. 2), 95-105. MR 0921933 (89c:76024)

5.
Lamb, H., Hydrodynamics, Cambridge University Press, 1932. MR 1317348 (96f:76001)

6.
Maxwell, C., Scientific Papers of Clark Maxwell, vol 2, p.1, Dover, New York, 1860.

7.
Serrin, J., Mathematical Principles of Classical Fluid Mechanics, sections 58-65. Handbuch der Physik VIII/1, Springer-Verlag, 1959. MR 0108116 (21:6836b)

8.
Truesdell, C., & R. Toupin, The Classical Field Theories, pp. 492-530. Handbuch der Physik III/1, Springer-Verlag, 1960. MR 0118005 (22:8778)

9.
Truesdell, C., The Mechanical Foundations of Elasticity and Fluid Dynamics, Gordon and Breach, 1966. MR 0192962 (33:1187a)

10.
Truesdell, C., The Elements of Continuum Mechanics, Springer-Verlag, 1966. MR 0214315 (35:5166)

11.
Weatherburn, C. E., Differential Geometry of Three Dimensions, Vol. 1, Cambridge University Press, 1955.

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Additional Information:

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

PII: S0033-569X-05-00966-1
Keywords: Navier-Stokes equations, boundary conditions, entropy condition
Received by editor(s): June 30, 2004
Posted: April 11, 2005
Copyright of article: Copyright 2005, Brown University


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