2004/11/17 by S. Piekarski, Piekarski, S.
Physics and Astronomy · #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #General Physics (physics.gen-ph) #physics.flu-dyn #physics.gen-ph
paper · pdf · doi:10.48550/arxiv.physics/0411154
arxiv created 2004/11/17 · arxiv updated 2009/12/01
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".