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Analysis of fluid equations by group methods

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Summary

Using the machinery of Lie-group analysis several equations arising in fluid mechanics are studied. In particular, the Burgers' equation, the KdV equation, the Hopf equation, the two-dimensional KdV equation and the Lin-Tsien equation are analyzed. In all cases the particular group includes arbitrary functions of time which permit the transformation of time-dependent equations into the corresponding time-independent ones. Infinitely many time-dependent solutions are associated with each steady solution. Some solutions are constructed.

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Author notes

  1. M. C. Nucci

    Present address: Dipartimento di Matematica, Universitá di Perugia, 06100, Perugia, Italy

Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, 30332, Atlanta, GA, USA

    W. F. Ames & M. C. Nucci

Authors
  1. W. F. Ames
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  2. M. C. Nucci
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Additional information

Research supported by U.S. Army Grant DAAG-29-84-K-0083.

Research supported by a NATO-CNR fellowship.

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Ames, W.F., Nucci, M.C. Analysis of fluid equations by group methods. J Eng Math 20, 181–187 (1986). https://doi.org/10.1007/BF00042776

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  • DOI: https://doi.org/10.1007/BF00042776

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