On Galilei-covariant Lagrangian models of fluids

Abstract

We use a covariant-like formulation of Galilei invariance in five dimensions to obtain a model for compressible irrotational barotropic fluids with pressure proportional to the square of the mass density. Some solutions for the one-dimensional version of one of these equations are found by using their Lie point symmetries. Other models of fluids are also discussed. Our purpose is to illustrate how the Galilei-covariant formalism can serve as a guide for the construction of non-relativistic wave equations relevant in many-body theories.