Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

Stability and uniqueness for a turbulence model of Burgers


Authors: C. O. Horgan and W. E. Olmstead
Journal: Quart. Appl. Math. 36 (1978), 121-127
MSC: Primary 76.35; Secondary 35Q99
DOI: https://doi.org/10.1090/qam/495602
MathSciNet review: 495602
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Abstract: In his early work on mathematical models of turbulence, J. M. Burgers proposed a nonlinear system, coupling an ordinary and a partial differential equation, to simulate flow in a channel. The now well-known Burgers equation arose in his work from a simplification of this system. The original system has some interesting features not shared by the Burgers equation. This investigation establishes results on the stability of the ``laminar'' stationary solution and uniqueness of the nonstationary solution of the system.


References [Enhancements On Off] (What's this?)

  • [1] J. M. Burgers, Mathematical examples illustrating relations occurring in the theory of turbulent fluid motion, Trans. Roy. Neth. Acad. Sci. Amsterdam 17, 1-53 (1939)
  • [2] J. M. Burgers, A mathematical model illustrating the theory of turbulence, in Advances in Applied Mechanics (R. von Mises and T. von Kármán, editors) 1, Academic Press, New York, 1948, pp. 171-199 MR 0027195
  • [3] E. R. Benton and G. W. Platzman, A table of solutions of the one-dimensional Burgers equation, Quart. Appl. Math. 30, 195-212 (1972) MR 0306736
  • [4] W. Eckhaus, Studies in non-linear stability theory, Springer Tracts in Natural Philosophy, Vol. 6, Springer-Verlag, Berlin, 1965 MR 0196298
  • [5] C. Golia and J. M. Abel, Path integral synthesis of Lyapunov functionals for partial differential equations, Int. J. Non-Linear Mech. 10 333-344 (1975) MR 0430489

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DOI: https://doi.org/10.1090/qam/495602
Article copyright: © Copyright 1978 American Mathematical Society

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