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Parametrization of the two and three-dimensional motion of a viscous incompressible liquid
Author(s):
K.
B.
Ranger
Journal:
Quart. Appl. Math.
64
(2006),
401-412.
MSC (2000):
Primary 76-xx, 76Dxx
Posted:
August 17, 2006
MathSciNet review:
2259045
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Additional information
Abstract:
A method is described for parametrizing the velocity components and space coordinates in terms of parametric functions and time for the two and three-dimensional motion of a viscous incompressible liquid. The two-dimensional motion contains four functions and the three-dimensional motion contains six functions satisfying minimal requirements.
References:
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- 1.
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- 2.
- R. Von Mises, Mathematical Theory of Compressible Fluid Flow, Applied Mathematics and Mechanics, vol. 3, Academic Press, New York, 1958, p. 85. MR 0094996 (20:1504)
- 3.
- G. Birkhoff and S. Mac Lane, A Survey of Modern Algebra, Macmillan Company of New York, 1941, p. 306. MR 0005093 (3:99h)
- 4.
- R. Berker, Intégration des équations du mouvement d'un fluide visqueux incompressible, Handbuch der Physik VIII/2, Springer, Berline, 1963, pp. 1-386. MR 0161513 (28:4717)
- 5.
- K. B. Ranger, Fluid velocity fields derived from vorticity singularities, Quart. Appl. Math. 62 (2004), 671-685. MR 2104268 (2005f:76035)
- 6.
- K. B. Ranger, Parametric solutions for differential equations, submitted for publication 2006.
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Additional Information:
K.
B.
Ranger
Affiliation:
Department of Mathematics, University of Toronto, Toronto, Ontario M5S 3G3 Canada
PII:
S0033-569X-06-01037-2
Received by editor(s):
May 12, 2004
Posted:
August 17, 2006
Copyright of article:
Copyright
2006,
Brown University
The copyright for this article reverts to public domain after 28 years from publication.
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