Perfect fluid dynamics with conformal Newton-Hooke symmetries

TL;DR

This paper develops perfect fluid equations invariant under the conformal Newton-Hooke group for any parameter value, constructs conserved charges for a specific case, and establishes a Hamiltonian framework.

Contribution

It introduces a novel class of perfect fluid equations with conformal Newton-Hooke symmetry applicable to arbitrary parameter values and provides a Hamiltonian formulation for a special case.

Findings

Invariant fluid equations under conformal Newton-Hooke group for all b5 values

Construction of conserved charges for b5=3/2

Hamiltonian formulation for b5=3/2

Abstract

Perfect fluid equations are formulated which are invariant under the $\ell$-conformal Newton-Hooke group for an arbitrary integer or half-integer value of the parameter $\ell$. For $\ell=\frac32$ the corresponding conserved charges are constructed and the Hamiltonian formulation is built.