Symmetries of fluid dynamics with polytropic exponent

Abstract The symmetries of the general Euler equations of fluid dynamics with polytropic exponent are determined using the Kaluza–Klein type framework of Duval et al. In the standard polytropic case the recent results of O'Raifeartaigh and Sreedhar are confirmed. Similar results are proved for polytropic exponent γ=−1, which corresponds to the dimensional reduction of d-branes. The relation between the duality transformation used in describing supernova explosion and cosmology is explained.