Perfect fluid dynamics with conformal Newton-Hooke symmetries

TL;DR

The paper addresses constructing perfect-fluid dynamics invariant under the $\ell$-conformal Newton-Hooke group for integer or half-integer $\ell$, by deforming the Euler equation to a Pais-Uhlenbeck–type operator and deriving a Hamiltonian with explicit conserved charges for $\ell=\tfrac{3}{2}$. It shows that Niederer-type transformations connect these NH-invariant equations to the $\ell$-conformal Galilei case, enabling a general construction for arbitrary $\ell$ through coset realizations and transformations. The main contributions are the explicit $\ell=\tfrac{3}{2}$ NH-symmetric fluid model, its Ostrogradski Hamiltonian, and the complete set of conserved charges realizing the conformal Newton-Hooke algebra, along with a Niederer recursion to higher $\ell$. This work advances non-relativistic holography and conformal fluid dynamics by incorporating a cosmological constant and providing concrete, analyzable models with clear symmetry algebras.

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.