Parametrization of the two and three-dimensional motion of a viscous incompressible liquid
Author:
K. B. Ranger
Journal:
Quart. Appl. Math. 64 (2006), 401-412
MSC (2000):
Primary 76-xx, 76Dxx
DOI:
https://doi.org/10.1090/S0033-569X-06-01037-2
Published electronically:
August 17, 2006
MathSciNet review:
2259045
Full-text PDF Free Access
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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.
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- Richard von Mises, Mathematical theory of compressible fluid flow, Academic Press, Inc., New York, N.Y., 1958. Applied mathematics and mechanics. Vol. 3. MR 0094996
- Garrett Birkhoff and Saunders MacLane, A Survey of Modern Algebra, Macmillan Company, New York, 1941. MR 0005093
- Ratip Berker, Intégration des équations du mouvement d’un fluide visqueux incompressible, Handbuch der Physik, Bd. VIII/2, Springer, Berlin, 1963, pp. 1–384 (French). MR 0161513
- K. B. Ranger, Fluid velocity fields derived from vorticity singularities, Quart. Appl. Math. 62 (2004), no. 4, 671–685. MR 2104268, DOI https://doi.org/10.1090/qam/2104268
6 K. B. Ranger, Parametric solutions for differential equations, submitted for publication 2006.
1 W.F. Ames, Nonlinear Partial Differential Equations in Engineering, Vol. II, Academic Press, 1972, p. 38.
2 R. Von Mises, Mathematical Theory of Compressible Fluid Flow, Applied Mathematics and Mechanics, vol. 3, Academic Press, New York, 1958, p. 85.
3 G. Birkhoff and S. Mac Lane, A Survey of Modern Algebra, Macmillan Company of New York, 1941, p. 306.
4 R. Berker, Intégration des équations du mouvement d’un fluide visqueux incompressible, Handbuch der Physik VIII/2, Springer, Berline, 1963, pp. 1–386.
5 K. B. Ranger, Fluid velocity fields derived from vorticity singularities, Quart. Appl. Math. 62 (2004), 671–685.
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
Received by editor(s):
May 12, 2004
Published electronically:
August 17, 2006
Article copyright:
© Copyright 2006
Brown University
The copyright for this article reverts to public domain 28 years after publication.
