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References
T. N. Abbot & K. Walters, Rheometrical flow systems, Part 2. Theory for the orthogonal rheometer, including an exact solution of the Navier-Stokes equations, J. Fluid. Mech. 40, 205–213 (1970).
G. K. Batchelor, Note on a class of solutions of the Navier-Stokes equations representing steady rotationally-symmetric flow, Quart. J. Mech. Appl. Math. 4, 29–41 (1951).
R. Berker, A new solution of the Navier-Stokes equation for the motion of a fluid contained between two parallel planes rotating about the same axis, Archiwum Mechaniki Stosowanej 31, 265–280 (1979).
R. Berker, Sur quelques cas d'intégration des équations du mouvement d'un fluide visqueux incompressible, Lille, Paris (1936).
J. H. Cerutti, Collocation Methods for Systems of Ordinary Differential Equations and Parabolic Partial Differential Equations, Thesis, University of Wisconsin (1975).
A. R. Elcrat, On the swirling flow between rotating coaxial disks, J. Differential Equations 18, 423–430 (1975).
J. D. Goddard, The dynamics of simple fluids in steady circular shear, Quarterly of Applied Mathematics 31, 107–118 (1983).
S. P. Hastings, On existence theorems for some problems from boundary layer theory, Arch. Rational Mech. Anal. 38, 308–316 (1970).
T. von Karman, Über laminare und turbulente Reibung, Z. Angew. Math. Mech. 1, 232–252 (1921).
H. O. Kreiss & S. V. Parter, On the swirling flow between rotating coaxial disks: existence and nonuniqueness, Communs. Pure and Applied Math. 36, 55–84 (1983).
J. B. McLeod & S. V. Parter, On the flow between two counter-rotating infinite plane disks, Arch. Rational Mech. Anal. 54, 301–327 (1974).
S. V. Parter, On the swirling flow between rotating coaxial disks: A survey, pages 258–280 in Theory and Applications of Singular Perturbations, Proc. of a Conf. Oberwolfach 1981, Edited by W. Eckhaus and E. M. deJager. Lecture Notes in Mathematics # 942, Springer-Verlag; Berlin, Heidelberg, New York (1982).
K. R. Rajagopal, On the flow of a simple fluid in an orthogonal rheometer, Arch. Rational Mech. Anal. 79, 29–47 (1982).
K. R. Rajagopal, A class of exact solutions to the Navier-Stokes equations, Int. J. Eng. Science, in press.
K. R. Rajagopal & A. S. Gupta, Flow and stability of a second grade fluid between two parallel plates rotating about non-coincident axes. Intl. J. Eng. Science 19, 1401–1409 (1981).
K. R. Rajagopal & A. S. Gupta, Flow and stability of second grade fluids between two parallel rotating plates, Archiwum Mechaniki Stosowanej 33, 663–674 (1981).
K. R. Rajagopal & A. S. Wineman, On the flow of a BKZ fluid in an orthogonal rheometer, Journal of Rheology 27, 509–516 (1983).
H. Rasmussen, A note on the non-unique solutions for the flow between two infinite rotating disks, Z. Angew. Math. Mech. 53, 273–274 (1973).
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Dedicated to Professor J. L. Ericksen on his 60th Birthday
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Parter, S.V., Rajagopal, K.R. Swirling flow between rotating plates. Arch. Rational Mech. Anal. 86, 305–315 (1984). https://doi.org/10.1007/BF00280030
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DOI: https://doi.org/10.1007/BF00280030