Quarterly of Applied Mathematics Quarterly of Applied Mathematics
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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
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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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W.F. Ames, Nonlinear Partial Differential Equations in Engineering, Vol. II, Academic Press, 1972, p. 38. MR 0473442 (57:13108)

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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)

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G. Birkhoff and S. Mac Lane, A Survey of Modern Algebra, Macmillan Company of New York, 1941, p. 306. MR 0005093 (3:99h)

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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)

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K. B. Ranger, Fluid velocity fields derived from vorticity singularities, Quart. Appl. Math. 62 (2004), 671-685. MR 2104268 (2005f:76035)

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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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