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Burger's equation: Generalizations and solutions

  • Kenneth M. Case
Conference paper
Part of the Lecture Notes in Physics book series (LNP, volume 12)

Abstract

We have seen that there exist generalizations of Burgers' equation which admit closed form solutions. The analog of the terms added to the original Burgers equation is the inclusion of forcing terms in the Navier-Stokes equation.

A number of directions for future work are suggested. From the connection with the Schrödinger equation we know there are other soluble models. For example, the case of a plane electromagnetic wave incident on a charged particle can be handled. It would be of some interest to apply the various approximate and statistical techniques which have been used on the Navier-Stokes equation to our soluble model equations.

In this connection it may be mentioned that there a re other model equations due to Burgers(4) which, when suitably modified5 yield simple solutions. Similar remarks hold for these equations.

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References

  1. 1.
    H. Bateman, “Some Recent Researches On The Motion of Fluids”, Mon. Weather Per. 43, pp. 163–170 (1915).Google Scholar
  2. 1a.
    J. M. Burgers, “Application of a Model System to Illustrate Some Points of the Statistical Theory of Turbulence”, Proc. Roy. Netherl. Academy of Sciences (Amsterdam) 43, p. 8, (1940).Google Scholar
  3. 2.
    E. Hopf, Comm. Pure and Applied Math. 3, pp. 201–230 (1950).Google Scholar
  4. 3.
    J. D. Cole, Quart. of Applied Math. 9, pp. 225–236 (1951).Google Scholar
  5. 4.
    J. M. Burgers, Vert. Nederl. Akad. Wetersch. Afd. Natuurk (Amsterdam) 17, 1, (1939).Google Scholar
  6. 5.
    K. M. Case and S. C. Chiu, “The Physics of Fluids” 12, 1799, (1969).Google Scholar

Copyright information

© Springer-Verlag 1972

Authors and Affiliations

  • Kenneth M. Case
    • 1
    • 2
  1. 1.The Rockefeller UniversityNew York
  2. 2.Institute for Defense AnalysesArlington

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