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Two-dimensional subsonic flows of a compressible fluid and their singularities


Author: Stefan Bergman
Journal: Trans. Amer. Math. Soc. 62 (1947), 452-498
MSC: Primary 76.1X
DOI: https://doi.org/10.1090/S0002-9947-1947-0026498-1
Erratum: Trans. Amer. Math. Soc. 63 (1948), 599-600.
MathSciNet review: 0026498
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  • [1] L. Ahlfors, Untersuchungen zur Theorie der konformen Abbildung der ganzen Funktionen. Acta Societatis scientiarum Fennica N.S. vol. 1 (1930).
  • [2] -, Zur Theorie der Überlagerungsflächen, Acta Math. vol. 65 (1935) pp. 157-194. MR 1555403
  • [3] Stefan Bergman, The hodograph method in the theory of compressible fluid, Supplement to Fluid dynamics by von Mises and Friedrichs, Brown University, 1941-1942.
  • [4] -, Partial differential equations, advanced topics (Conformal mapping of multiply connected domains), Brown University, 1941.
  • [5] -, A formula for the stream function of certain flows, Proc. Nat. Acad. Sci. U.S.A. vol. 29 (1943) pp. 276-281. MR 0010079 (5:247c)
  • [6] -, Residue theorems of harmonic functions of three variables, Bull. Amer. Math. Soc. vol. 49 (1943) pp. 163-174. MR 0007556 (4:159c)
  • [7] -, On two-dimensional flows of compressible fluids, Technical Note 972, National Advisory Committee for Aeronautics, 1945, pp. 1-81. MR 0014874 (7:342g)
  • [8] -, Graphical and analytical methods for the determination of a flow of a compressible fluid around an obstacle, Technical Note 973, National Advisory Committee for Aeronautics, 1945, pp. 1-29. MR 0014875 (7:343a)
  • [9] -, Certain classes of analytic functions of two real variables and their properties, Trans. Amer. Math. Soc. vol. 57 (1945) pp. 299-331. MR 0012370 (7:16f)
  • [10] -, Methods for the determination and computation of flow patterns of a compressible fluid, Technical Note 1018, National Advisory Committee for Aeronautics, 1946, pp. 1-71. MR 0018506 (8:295b)
  • [11] L. Bers and A. Gelbart, On a class of differential equations in mechanics of continua, Quarterly of Applied Mathematics vol. 1 (1943) pp. 168-188. MR 0008556 (5:25b)
  • [12] -, On a class of functions defined by partial differential equations, Trans. Amer. Math. Soc. vol. 56 (1944) pp. 67-93. MR 0010910 (6:86f)
  • [13] S. A. Chaplygin, On gas jets, Scientific Memoirs, Moscow University, Physico-Mathematical Section vol. 21 (1904) pp. 1-127. (Trans, by M. Slud, Brown University, 1944, or Technical Memorandum 1063, National Advisory Committee for Aeronautics, 1944.) MR 0015979 (7:495h)
  • [14] J. B. Diaz, On a class of partial differential equations of even order, Amer. J. Math. vol. 68 (1946) pp. 611-659. MR 0019828 (8:466d)
  • [15] H. Kraft and C. Dibble, Some two-dimensional adiabatic compressible flow patterns, Journal of Aeronautical Science vol. 11 (1944) pp. 283-298.
  • [16] M. Lavrentieff, Sur une classe de représentations continues, C. R. Acad. Sei. Paris vol. 200 (1935) pp. 1010-1012.
  • [17] -, Sur une classe de représentations continues, Rec. Math. (Mat. Sbornik) N.S. vol. 42 (1935) pp. 407-424.
  • [18] P. Molenbroek, Über einige Bewegungen eines Gases mit Annahme eines Geschwindigkeits potentials, Archiv der Mathematik und Physik (2) vol. 9 (1890) pp. 157-195.
  • [19] F. Ringleb, Exakte Lösungen der Differentialgleichungen einer adiabatischen Gasströmung, Zietschrift für angewandte Mathematik und Mechanik vol. 20 (1940) pp. 188-198. MR 0003140 (2:169e)
  • [20] T. von Kármán, Compressibility effects in aerodynamics, Journal of Aeronautical Science vol. S (1941) pp. 337-356. MR 0005848 (3:220b)
  • [21] R. von Mises, Theory of flight, McGraw-Hill publications in Aeronautical Science, New York, 1945.
  • [22] -, Integral theorems in three-dimensional potential flow, Bull. Amer. Math. Soc. vol. 50 (1944) pp. 599-611. MR 0010834 (6:76f)
  • [23] R. von Mises and K. Friedrichs, Fluid dynamics, Lecture Notes, Brown University, 1941.

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DOI: https://doi.org/10.1090/S0002-9947-1947-0026498-1
Article copyright: © Copyright 1947 American Mathematical Society

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