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Pre-Publicación 2011-01

Alfredo Bermúdez, Rafael Muñoz-Sola, Carlos Reales, Rodolfo Rodríguez, Pilar Salgado:

A proof of the Reynolds transport theorem in the space $W^{1,1}(Q)$. Extension to cylindrical coordinates

Abstract:

In this Note we give a proof of the Reynolds transport theorem for the case where the field belongs to the space $W^{1,1}(Q)$, Q being the trajectory under a motion of a reference configuration which is a bounded open subset of $R^n$. We first consider the standard formula in Cartesian coordinates. Next, a particular version in three-dimensional cylindrical coordinates for an axisymmetric field and an axisymmetric motion keeping invariant the azimuthal coordinate is proved.

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