On the invariant formulation of fluid mechanics
Fluid Dynamics
2007-05-23 v1 General Physics
Abstract
It can be observed that the differential operators of fluid mechanics can be defined in terms of the complete derivative on the finite - dimensional affine space. It follows from the fact that all norms on the finite - dimensional vector space are equivalent and from the definition of the complete derivative on the normed affine spaces (see: L.Schwartz, Analyse Mathematique, Hermann, 1967). In particular, it is shown that the "substantial derivative" of the standard formulation is a directional derivative along the "non - relativistic four - velocity".
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Cite
@article{arxiv.physics/0411154,
title = {On the invariant formulation of fluid mechanics},
author = {S. Piekarski},
journal= {arXiv preprint arXiv:physics/0411154},
year = {2007}
}