Symmetries of fluid dynamics with polytropic exponent

The symmetries of the general Euler equations of fluid dynamics with polytr opic exponent are determined using the Kaluza-Klein type framework of Duval et al. In the standard polytropic case the recent results of O'Raifeartaig h and Sreedhar are confirmed. Similar results are proved for polytropic exp onent gamma = -1, which corresponds to the dimensional reduction of d-brane s. The relation between the duality transformation used in describing super nova explosion and cosmology is explained. (C) 2001 Elsevier Science B.V. A ll rights reserved.