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

$f_{\theta\theta}+ \frac{v^2}{1-\frac{v^2}{c^2}}f_{vv}+v f_v=0.$

Here, $c=c(v)$ is the speed of sound, determined by the equation of state of the fluid and conservation of energy.

References

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