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Categories: Partial differential equations | Equations

Chaplygin's equation

In mathematics, Chaplygin's equation is a nonlinear partial differential equation useful in the study of transonic flow.

It is

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

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

The equation is named for Sergei Alekseevich Chaplygin.

Categories: Partial differential equations | Equations

01-04-2007 01:18:14
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