Lagrangian fluid mechanics

TL;DR

This paper applies the method of Lagrangians with covariant derivatives to derive Euler-Lagrange equations and energy-momentum tensors for scalar and vector fields in a covariant framework.

Contribution

It introduces a specific application of MLCD to fields depending on covariant derivatives, deriving fundamental equations and tensors.

Findings

Derived Euler-Lagrange equations for scalar and vector fields.

Obtained energy-momentum tensors using covariant Noether's identities.

Provided a framework for covariant Lagrangian field theories.

Abstract

The method of Lagrangians with covariant derivative (MLCD) is applied to a special type of Lagrangian density depending on scalar and vector fields as well as on their first covariant derivatives. The corresponding Euler-Lagrange's equations and energy-momentum tensors are found on the basis of the covariant Noether's identities.