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.
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- Carmine Golia and Jacob M. Abel, Path integral synthesis of Lyapunov functionals for partial differential equations, Internat. J. Non-Linear Mech. 10 (1975), no. 6, 333–345 (English, with French and German summaries). MR 430489, DOI https://doi.org/10.1007/bf02149031
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)
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
E. R. Benton and G. W. Platzman, A table of solutions of the one-dimensional Burgers equation, Quart. Appl. Math. 30, 195–212 (1972)
W. Eckhaus, Studies in non-linear stability theory, Springer Tracts in Natural Philosophy, Vol. 6, Springer-Verlag, Berlin, 1965
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)
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Article copyright:
© Copyright 1978
American Mathematical Society
