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Abstract: Phase-space Lagrangian dynamics in ideal fluids i.e, continua is usuallyrelated to the so-called {\it ideal tracer particles}. The latter, which can inprinciple be permitted to have arbitrary initial velocities, are understood asparticles of infinitesimal size which do not produce significant perturbationsof the fluid and do not interact among themselves. An unsolved theoreticalproblem is the correct definition of their dynamics in ideal fluids. The issueis relevant in order to exhibit the connection between fluid dynamics and theclassical dynamical system, underlying a prescribed fluid system, whichuniquely generates its time-evolution. \The goal of this paper is to show that the tracer-particle dynamics can be{\it exactly} established for an arbitrary incompressible fluid uniquely basedon the construction of an inverse kinetic theory IKT Tessarotto \textit{etal.}, 2000-2008. As an example, the case of an incompressible Newtonianthermofluid is here considered.

Autor: Marco Tessarotto, Claudio Cremaschini, Massimo Tessarotto



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