Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X



A general theorem concerning the stability of a particular non-Newtonian fluid

Author: Samuel M. Genensky
Journal: Quart. Appl. Math. 18 (1960), 245-250
MSC: Primary 76.00
DOI: https://doi.org/10.1090/qam/114478
MathSciNet review: 114478
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Abstract: It is the intention of the present paper to prove a theorem concerning the stability of a particular non-Newtonian fluid suggested to the author by Professor R. S. Rivlin of Brown University. The method used in proving this theorem is similar to that employed by H. Schlichting in his proof of a similar theorem for an inviscid fluid which was originally established by Lord Rayleigh. The acceleration gradients introduced by the non-Newtonian fluid model into the constitutive equations are found to alter the stability criterion set forth by Rayleigh for an inviscid fluid.

References [Enhancements On Off] (What's this?)

  • [1] Lord Rayleigh, On the stability or instability of certain fluid motions, I, Proc. Lond. Math. Soc. 9, 57-70 (1880); see also Scientific Papers 1, 474-487 (1899) MR 1576885
  • [2] H. Schlichting, Boundary layer theory, translated by J. Kestin, McGraw-Hill, Inc., New York, 1955, pp. 314-323 MR 0076530
  • [3] R. S. Rivlin, Further remarks on the stress--deformation relations for isotropic materials, J. Ratl. Mech. and Anal. 4, 681-702 (1955) MR 0071980
  • [4] R. S. Rivlin, Solutions of some problems in the exact theory of visco-elasticity, J. Ratl. Mech. and Anal. 5, 179-188 (1956) MR 0075739

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DOI: https://doi.org/10.1090/qam/114478
Article copyright: © Copyright 1960 American Mathematical Society

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