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?
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1$\begingroup$ From EOM: "[quasiconformal mappings] are also naturally connected with problems on streamline flows of subsonic gas dynamics, just as conformal mappings satisfying the Cauchy–Riemann system are connected with the flow of an incompressible ideal fluid (see [9], [31])." See the reference [9] in particular: "Mathematical aspects of subsonic and transonic gas dynamics" by Bers. $\endgroup$– user147263Feb 2, 2015 at 3:19
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$\begingroup$ That said, I don't think this line of research is under active development now. $\endgroup$– user147263Feb 2, 2015 at 3:33
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$\begingroup$ Thank you very much for the information! $\endgroup$– BraindeadFeb 2, 2015 at 3:55
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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.
Some references:
- 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.