Conservation laws of the one-dimensional equations of relativistic gas dynamics in Lagrangian coordinates

Abstract

The present paper is focused on the analysis of the one-dimensional relativistic gas dynamics equations. The studied equations are considered in Lagrangian description, making it possible to find a Lagrangian such that the relativistic gas dynamics equations can be rewritten in a variational form. Complete group analysis of the Euler-Lagrange equation is performed. The symmetries found are used to derive conservation laws in Lagrangian variables by means of Noether's theorem. The analogs of the newly found conservation laws in Eulerian coordinates are presented as well.

Lie groups and continuum mechanics: where do we stand today?

“…Moreover, Noether's theorem was used to study schocks [88] or to show the non-existence of time-periodic solutions with finite nonzero energy [87]. Some other recent applications in fluid dynamics are proposed in [89][90][91][92][93][94]. Exploitation of Noether's theorem for modelling and stability analysis in cosmology can be found in [60,61].…”