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Steady extension of incompressible simple fluids. (English) Zbl 0131.40801

Keywords:
fluid mechanics
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[1] Noll, Arch. Rat. Mech. Anal. 2 pp 197– (1958)
[2] Reiner, Am. J. Math. 67 pp 350– (1945)
[3] Rivlin, Proc. Roy. Soc. (London) A193 pp 260– (1948)
[4] Rivlin, J. Rat. Mech. Anal. 4 pp 323– (1955)
[5] Rivlin, J. Rat. Mech. Anal. 5 pp 179– (1956)
[6] Coleman, Revs. Modern Phys. 33 pp 239– (1961)
[7] Lodge, Trans. Faraday Soc. 52 pp 120– (1956)
[8] Coleman, Arch. Rat. Mech. Anal. 3 pp 289– (1959)
[9] Coleman, J. Appl. Phys. 30 pp 1508– (1959)
[10] Coleman, Ann. N.Y. Acad. Sci. 89 pp 672– (1961)
[11] Coleman, Arch. Rat. Mech. Anal. 9 pp 273– (1962)
[12] Among the viscometric flows there are also some physically usefulapproximatesolutions to the dynamical equations such as torsional flow and cone and plate flow.
[13] Definitions and an introduction to the theory of substantially stagnant motions and viscometric flows are given in reference 11.
[14] Thenth-order Rivlin-Ericksen tensor furnishes a properly invariant measure of thenth time derivative of the ”strain.” For viscometric flows all Rivlin-Ericksen tensors of order greater than 2 are zero.
[15] See also reference 10.
[16] A statement and proof of that theorem is given by J. Serrin in S. Flügge,Handbuch der Physik(Springer-Verlag, Berlin, 1959), Vol. VIIII (Fluid Mechanics I), pp. 125–263.
[17] The relationship between the principle of positive internal production of entropy and the sign of the power dissipation in simple fluids is discussed in reference 11.
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