Perfect fluid equations with nonrelativistic conformal symmetry: Exact solutions

TL;DR

This paper constructs exact solutions to perfect fluid equations with nonrelativistic conformal symmetries, revealing how to achieve high densities briefly by tuning parameters.

Contribution

It introduces a group-theoretic method to find exact solutions invariant under various nonrelativistic conformal groups, extending understanding of fluid dynamics symmetry.

Findings

Exact solutions resemble Bjorken flow patterns.

High density states can be achieved temporarily by parameter adjustment.

Solutions are invariant under Schrodinger, l-conformal Galilei, and Lifshitz groups.

Abstract

The group-theoretic approach is used to construct exact solutions to perfect fluid equations invariant under the Schrodinger group, or the l-conformal Galilei group, or the Lifshitz group. In each respective case, the velocity vector field looks similar to the Bjorken flow. It is shown that one can reach an arbitrarily high density (and hence pressure) for a short period of time by adjusting the value of l and other free parameters available.