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Bergman’s Linear Integral Operator Method in the Theory of Compressible Fluid Flow pp 76–90Cite as

Singularities

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Abstract

As mentioned above, singularities play an important role in hodograph transformations. In a brief résumé of Bergman’s method given in the present work, it is impossible to discuss all the details and items on the subject of singularities. Hence, below only general and more important features will be briefly outlined. A reader, advanced in mathematics, may find more details in the original literature, particularly in6.

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Notes

  1. S. Bergman: Determination of axially symmetric flow patterns of a compressible fluid. J. Math. Physics 29, 133–145 (1950).

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  2. G. S. S. Ludford: The behavior at infinity of the potential function of the flow of a perfect gas in two dimensions. Report 23a, Nav. Res. Contr. N5ori 76/XVI NR 043 046, Harvard Univ. (1950). — Two notes on the singularities of a compressible flow in the pseudo-logarithmic plane. Report 23b, Nav. Res. Contr. N5ori 76/XVI NR 043 046, Harvard Univ. (1950).

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  3. G. S. S. Ludford: The behavior at infinity of the potential function of a two-dimensional subsonic compressible flow. Report 23, Nav. Res. Contr. N5ori 76/XVI NR 043 046, Harvard Univ., J. Math. Physics 30, (3), 117–130 (1951).

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  4. S. Bergman: The hodograph method in the theory of compressible fluids. Supplement to “Fluid Dynamics” by R. v. Mises and K. O. Friedrichs, Brown University (1941/42).

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  5. S. Bergman: A formula for the stream function of certain flows. Proc. Nat. Acad. Sci., U. S.A. 29, 276–281 (1943).

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  6. L. Bers and A. Gelbart: On a class of differential equations in mechanics of continua. Quart. Appl. Math. 1, 168–188 (1943).

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  7. L. Bers and A. Gelbart: On a class of functions defined by partial differential equations. Trans. Amer. Math. Soc. 56, No. 1, 67–93 (1944).

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  8. S. Bergman: Certain classes of analytic functions of two real variables and their properties. Trans. Amer. Math. Soc. 57, 299–331 (1945).

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  9. S. Bergman: Two-dimensional subsonic flows of a compressible fluid and their singularities. Trans. Amer. Math. Soc. 61, 452–498 (1947).

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  10. S. Bergman: On two-dimensional flows of compressible fluids. N. A. C. A., T. N. No. 972 (1945).

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  11. S. Bergman: On tables for the determination of transonic flow patterns. Hans Reissner Anniversary Volume: Contributions to Applied Mechanics. J. W. Edwards (1949).

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Author information

Authors and Affiliations

  1. Fluid Dynamics Panel University of Illinois, Urbana, Illinois, USA

    M. Z. v. Krzywoblocki Sc. D. (Lille), Ph. D. (Brooklyn), M. A. (Math., Stanford), M. S. (Appl. Math., Brown) M. Aer. En. (Brooklyn), Dipl. Ing. (Lemberg) (Professor)

Authors
  1. M. Z. v. Krzywoblocki Sc. D. (Lille), Ph. D. (Brooklyn), M. A. (Math., Stanford), M. S. (Appl. Math., Brown) M. Aer. En. (Brooklyn), Dipl. Ing. (Lemberg)
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© 1960 Springer-Verlag Wien

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v. Krzywoblocki, M.Z. (1960). Singularities. In: Bergman’s Linear Integral Operator Method in the Theory of Compressible Fluid Flow. Springer, Vienna. https://doi.org/10.1007/978-3-7091-3994-3_7

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  • DOI: https://doi.org/10.1007/978-3-7091-3994-3_7

  • Publisher Name: Springer, Vienna

  • Print ISBN: 978-3-7091-3995-0

  • Online ISBN: 978-3-7091-3994-3

  • eBook Packages: Springer Book Archive

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