Archive for Rational Mechanics and Analysis

, Volume 14, Issue 1, pp 1–26

Certain non-steady flows of second-order fluids

  • Tsuan Wu Ting
Article

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References

  1. [1]
    Reiner, M.: A mathematical theory of dilatancy. Amer. J. Math. 67, 350–362 (1945).MathSciNetCrossRefMATHGoogle Scholar
  2. [2]
    Rivlin, R. S.: The hydrodynamics of non-Newtonian fluids I. Proc. Roy. Soc., London, Ser. A 193, 260–281 (1948).ADSMathSciNetCrossRefMATHGoogle Scholar
  3. [3]
    Rivlin, R. S.: The hydrodynamics of non-Newtonian fluids II. Proc. Cambridge Phil. Soc. 45, 88–91 (1949).ADSMathSciNetCrossRefMATHGoogle Scholar
  4. [4]
    Truesdell, C.: A new definition of a fluid I. The Stokesian fluid. J. Math. Pures Appl. 29, 215–244 (1950).MathSciNetMATHGoogle Scholar
  5. [5]
    Truesdell, C.: A new definition of a fluid II. The Maxwellian fluid. J. Math. Pures Appl. 30, 111–158 (1951).MathSciNetMATHGoogle Scholar
  6. [6]
    Serrin, J.: The derivation of stress-strain relations for a Stokesian fluid. J. Math. and Mech. 8, 459–470 (1959).MATHGoogle Scholar
  7. [7]
    Serrin, J.: Poiseuille and Couette flow of non-Newtonian fluids. Z. Angew. Math. and Mech. 39, 295–299 (1959).MathSciNetCrossRefMATHGoogle Scholar
  8. [8]
    Noll, W.: A mathematical theory of the mechanical behavior of continuous media. Arch. Rational Mech. Anal. 2, 197–226 (1958).ADSMathSciNetCrossRefMATHGoogle Scholar
  9. [9]
    Coleman, B. D., & W. Noll: On certain steady flows of general fluids. Arch. Rational Mech. Anal. 3, 289–303 (1959).ADSMathSciNetCrossRefMATHGoogle Scholar
  10. [10]
    Coleman, B. D., & W. Noll: An approximation theorem for functionals with application in continuum mechanics. Arch. Rational Mech. Anal. 6, 355–370 (1960).ADSMathSciNetCrossRefMATHGoogle Scholar
  11. [11]
    Rivlin, R. S., & J. L. Ericksen: Stress-deformation relations for isotropic materials. J. Rational Mech. Anal. 4, 323–425 (1955).MathSciNetMATHGoogle Scholar
  12. [12]
    Truesdell, C., & R. Toupin: The classical field theories. Handbuch der Physik, Bd. III/1, pp. 543–545. Berlin-Göttingen-Heidelberg: Springer 1960.Google Scholar
  13. [13]
    Courant, R., & D. Hilbert: Methods of Mathematical Physics, Vol. 2, pp. 535–550, Vol. 1, pp. 351–362. New York: Interscience 1962.MATHGoogle Scholar
  14. [14]
    Gray, A., & B. Mathews: A Treatise on Bessel Functions and their Applications to Physics, Chap. V. VII, pp. XIII-XIV. London: Macmillan 1931.Google Scholar
  15. [15]
    Hobson, W.: The Theory of Functions of a Real Variable and the Theory of Fourier's Series, Vol. 1, pp. 425–426. New York: Dover 1957.Google Scholar
  16. [16]
    Lamb, H.: Hydrodynamics, pp. 592–593. New York: Dover 1945.Google Scholar
  17. [17]
    Dryden, H. L., F. D. Murnaghan & H. Bateman: Hydrodynamics, p. 196. New York: Dover 1956.MATHGoogle Scholar
  18. [18]
    Lamb, H. A.: A paradox in fluid motion, Aeronautical Research Comm., R. & M., No. 1084 (Ae 263); Annual Report, London, 1926–1927, pp. 78–81.Google Scholar

Copyright information

© Springer-Verlag 1963

Authors and Affiliations

  • Tsuan Wu Ting
    • 1
  1. 1.Courant Institute of Mathematical Sciences New-York UniversityNew York

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