Constructing the Lagrangian in the Eulerian coordinate for relativistic hydrodynamics
Journal
Physical Review E
Journal Volume
49
Journal Issue
2
Pages
1269-1272
Date Issued
1994
Author(s)
Abstract
The Lorentz-covariant Lagrangian for an ideal relativistic flow is constructed in the Eulerian coordinate. In contrast to the Lagrangian of nonrelativistic flows in the Eulerian formulation, for which the continuity equation is required to be externally imposed as a constraint [Mittag, Stephen, and Yourgrau, in Variational Principles in Dynamics .ul and Quantum Theory, edited by W. Yourgrau and X. Mandelstam (Dover, New York, 1968)], this Lorentz-covariant Lagrangian automatically yields the continuity equation as well as the equation of state. In addition, the relativistic generalization of the Bernoulli equation can also be derived from the present formulation.
Type
journal article