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Symmetry approach and exact solutions in hydrodynamics. (English) Zbl 1086.76060
Mladenov, Ivaïlo M.(ed.) et al., Proceedings of the 6th international conference on geometry, integrability and quantization, Sts. Constantine and Elena, Bulgaria, June 3–10, 2004. Sofia: Bulgarian Academy of Sciences (ISBN 954-84952-9-5/pbk). 191-202 (2005).
Summary: The application of symmetry analysis to hydrodynamics is illustrated by two examples. The first one is a description of all irrotational barochronous motions of ideal gas. The second is an exact solution of magnetohydrodynamics equations for infinitely conducting media, which describes the flow of the so called “special vortex” type.
MSC:
76M60Symmetry analysis, Lie group and algebra methods (fluid mechanics)
76N15Gas dynamics, general
76W05Magnetohydrodynamics and electrohydrodynamics