On the invariant formulation of fluid mechanics

S. Piekarski

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On the invariant formulation of fluid mechanics

S. Piekarski

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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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S. Piekarski. 2004-11-17. On the invariant formulation of fluid mechanics. https://arxiv.org/abs/physics/0411154

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