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 and generalized. Similar results are proved for polytropic exponent $\gamma =-1$, which corresponds to the dimensional reduction of $d$-branes. The relation between the duality transformation used in describing supernova explosion and Cosmology is explained.

10 pages, LaTex, no figures. Revised version: A new proof of the Schrodinger symmetry and two more references added. To appear in Phys. Lett. A

References in corpus (3)

• Celestial Mechanics, Conformal Structures, and Gravitational Waves
• Field-dependent symmetries of a non-relativistic fluid model
• Darboux class of cosmological fluids with time-dependent adiabatic indices

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