I know that conformal mappings can be used to study 2 dimensional fluid flows. But I was wondering how quasiconformal mapping have been applied in this respect?
The connection that I know of is that the transformation from the flow plane to the hodograph plane is quasiconformal under some assumptions on the flow. Conformal maps correspond to incompressible flow; quasiconformal to compressible.
- Two-dimensional subsonic flows of a compressible fluid and their singularities by Stefan Bergman; Trans. Amer. Math. Soc. 62 (1947), 452-498.
- Book "Mathematical aspects of subsonic and transonic gas dynamics" by Lipman Bers.
Search for "quasiconformal hodograph flow" to find a few more.