Chaplygin's equation

Chaplygin's equation

In mathematics, Chaplygin's equation, named after Sergei Alekseevich Chaplygin, is a partial differential equation useful in the study of transonic flow.[1] It is


\Psi_{\theta\theta}+
\frac{v^2}{1-\frac{v^2}{c^2}}\Psi_{vv}+v\Psi_v=0.

Here, c = c(v) is the speed of sound, determined by the equation of state of the fluid and Bernoulli's principle.

References

  1. ^ Landau, L. D.; Lifshitz, E. M. (1982). Fluid Mechanics (2 ed.). Pergamon Press. p. 432. 

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