Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

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A general formulation of the boundary conditions on the vector potential in three-dimensional hydrodynamics


Authors: G. J. Hirasaki and J. D. Hellums
Journal: Quart. Appl. Math. 26 (1968), 331-342
MSC: Primary 76.35
DOI: https://doi.org/10.1090/qam/234676
MathSciNet review: 234676
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References [Enhancements On Off] (What's this?)

  • [1] H. Lamb, A treatise on the mathematical theory of the motion of fluids, Cambridge University Press, New York, 1879
  • [2] Caius Jacob, Introduction mathématique à la mécanique des fluides, Préface de Henri Villat, Éditions de l’Académie de la République Populaire Roumaine, Bucharesst; Gauthier-Villars, Paris, 1959 (French). MR 0114422
  • [3] R. Timman, Le potentiel vecteur et son application à l’analyse harmonique d’un écoulement à trois dimensions, Mémoires sur la mécanique des fluides offerts à M. Dimitri P. Riabouchinsky, Publ. Sci. Tech. Ministère de l’Air, Tech. Ministère de l’Air, Paris, 1954, pp. 351–361 (French). MR 0065329
  • [4] Jean-Jacques Moreau, Une spécification du potentiel-vecteur en hydrodynamique, C. R. Acad. Sci. Paris 248 (1959), 3406–3408 (French). MR 0104412
  • [5] K. Aziz and J. D. Hellums, Numerical solution of the three-dimensional equations of motion for laminar natural convection, Phys. Fluids 10, 314 (1967)
  • [6] O. D. Kellogg, Foundations of potential theory, Dover, New York, 1953
  • [7] H. B. Phillips, Vector analysis, Wiley, New York, 1933
  • [8] G. J. Hirasaki, Ph.D. Thesis, Rice University, Houston, Texas, 1967
  • [9] R. Aris, Vectors, tensors, and the basic equations of fluid mechanics, Prentice-Hall, Englewood Cliffs, New Jersey, 1962
  • [10] Lipman Bers, Fritz John, and Martin Schechter, Partial differential equations, Lectures in Applied Mathematics, Vol. III, Interscience Publishers John Wiley & Sons, Inc. New York-London-Sydney, 1964. MR 0163043
  • [11] C. Truesdell, The classical field theories, Encyclopedia of Physics III, S. Flügge, ed., Springer-Verlag, Berlin, 1960

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DOI: https://doi.org/10.1090/qam/234676
Article copyright: © Copyright 1968 American Mathematical Society


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