dorsal/arxiv
View SchemaOn the invariant formulation of fluid mechanics
| Authors | S. Piekarski |
|---|---|
| Categories | |
| ArXiv ID | physics/0411154 |
| URL | https://arxiv.org/abs/physics/0411154 |
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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"abstract": "It can be observed that the differential operators of fluid mechanics can be\ndefined in terms of the complete derivative on the finite - dimensional affine\nspace. It follows from the fact that all norms on the finite - dimensional\nvector space are equivalent and from the definition of the complete derivative\non the normed affine spaces (see: L.Schwartz, Analyse Mathematique, Hermann,\n1967). In particular, it is shown that the \"substantial derivative\" of the\nstandard formulation is a directional derivative along the \"non - relativistic\nfour - velocity\".",
"arxiv_id": "physics/0411154",
"authors": [
"S. Piekarski"
],
"categories": [
"physics.flu-dyn",
"physics.gen-ph"
],
"title": "On the invariant formulation of fluid mechanics",
"url": "https://arxiv.org/abs/physics/0411154"
},
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