Symmetries of fluid dynamics with polytropic exponent

TL;DR

This paper investigates the symmetries of fluid dynamics equations with polytropic exponent using a Kaluza-Klein framework, confirming and extending recent results, and exploring special cases related to branes and cosmological dualities.

Contribution

It generalizes the understanding of symmetries in fluid dynamics with polytropic exponents, including special cases linked to branes and cosmological dualities.

Findings

Confirmed and extended symmetries for standard polytropic fluids.

Derived new symmetry results for the case b3=-1.

Connected fluid symmetries to brane dimensional reductions and cosmological dualities.

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 $\it{al}$. 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.