Chaplygin's equation

Summary

Chaplygin's equation is the linear partial differential equation of steady planar potential flow of a gas in hodograph variables. These variables are the speed and the flow angle. It comes from the hodograph transformation, which turns the nonlinear equations of compressible flow into linear ones. The equation is elliptic where the flow is subsonic and hyperbolic where it is supersonic. So it is a basic model of mixed type, related to the Tricomi equation. It is named after Sergey Chaplygin, who used it to study gas jets. See the definition.