Remarks on the Lie derivative in fluid mechanics

It is known that the invariance properties derived from Noether's theorem or associated with the Lie derivative can be adapted to fluid mechanics. The associated invariance groups are easily analyzed in a four-dimensional reference space representing the Lagrangian variables. A calculation method uses the Lie derivative associated with the velocity quadrivector in space-time. An interpretation of this derivative connects the space-time and the reference space; it allows to analyze the notion of tensor moving with the fluid and to find conservation laws and many invariance theorems in fluid mechanics.

Automated summary

It is possible to adapt the invariance properties derived from Noether's theorem or associated with the Lie derivative to fluid mechanics. By analyzing the invariance groups in a four-dimensional reference space representing the Lagrangian variables, a calculation method is utilized which involves the Lie derivative associated with the velocity quadrivector in space-time. This derivative allows for the connection between space-time and the reference space, enabling the analysis of tensor motion with the fluid and the discovery of conservation laws and invariance theorems in fluid mechanics.