Equations of fluid dynamics with the l-conformal Galilei symmetry

TL;DR

This paper formulates fluid dynamics equations invariant under the l-conformal Galilei group, extending classical equations with higher order derivatives and symmetry considerations, and identifies conserved charges related to this symmetry.

Contribution

It introduces a new class of fluid dynamics equations invariant under the l-conformal Galilei symmetry, including higher order derivatives and conserved charges.

Findings

Equations include a higher order Euler analogue.

Conservation laws associated with the symmetry are derived.

Modified equations of state are proposed.

Abstract

Equations of fluid dynamics are formulated, which hold invariant under the action of the l-conformal Galilei group. They include the conventional continuity equation, a higher order material derivative analogue of the Euler equation, and a suitable modification of the conventional equation of state. Conserved charges associated with the l-conformal Galilei symmetry transformations are presented.