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Kinetic theory of the impulsive motion of an infinite plane. (English) Zbl 0082.39503


Keywords:

fluid mechanics
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[1] Rayleigh, Phil. Mag. 21 pp 647– (1911)
[2] Scientific Papers(Cambridge University Press, New York, 1920), Vol. 6, p. 29.
[3] Sir James Jeans,The Dynamical Theory of Gases(Dover Publications, New York, 1954), p. 242. · Zbl 0031.09902
[4] Yang, J. Math. Phys. 35 pp 195– (1956) · Zbl 0072.42105
[5] Howarth, Quart. J. Mech. and Appl. Math. 4 pp 157– (1951)
[6] Grad, Communs. Appl. Math. 2 pp 331– (1949)
[7] U. Yvon, cf. p. 100 of V. Kourganoff,Basic Methods in Transfer Problems(Oxford University Press, New York, 1952).
[8] Gross, Astrophys. J. 123 pp 343– (1956)
[9] Gross, Ann. Phys. 1 pp 141– (1957)
[10] M. Knudsen,The Kinetic Theory of Gases(Methuen & Company, Ltd., London, 1934); · JFM 60.1420.10
[11] and E. Merlic, University of California, Report No. HE-150-141 (1956).
[12] S. Chapman and T. G. Cowling,The Mathematical Theory of Non-Uniform Gases(Cambridge University Press, New York, 1953). · Zbl 0063.00782
[13] S. Ziering, Ph.D. thesis, Syracuse University (1958);
[14] Gross, Phys. Fluids 1 pp 215– (1958)
[15] A treatment of the Rayleigh problem using the simple kinetic equation of reference 6 can be found in E. A. Jackson, Ph.D. thesis, Syracuse University (January, 1958). The results are in qualitative agreement with those found here.
[16] H. S. Carslaw and J. C. Jager,Operational Methods in Applied Mathematics(Oxford University Press, New York, 1949), second edition.
[17] Bateman Manuscript Project,Tables of Integral Transforms(McGraw-Hill Book Company, Inc., New York, 1954), Vol. I, or reference 12.
[18] Bhatnager, Phys. Rev. 94 pp 511– (1954)
[19] For an exact statement and proof of the inversion theorem, see reference 12, p. 299.
[20] See reference 2, p. 276, or reference 8, p. 218. Note that their viscosity is obtained by multiplying ours with the massmof the molecules.
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