Microscopic statistical description of incompressible Navier-Stokes granular fluids

作者: Massimo Tessarotto , Michael Mond , Claudio Asci

DOI: 10.1140/EPJP/I2017-11472-2

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摘要: Based on the recently established Master kinetic equation and related constant H-theorem which describe statistical behavior of Boltzmann-Sinai classical dynamical system for smooth hard spherical particles, problem is posed determining a microscopic description holding an incompressible Navier-Stokes fluid. The goal reached by introducing suitable mean-field interaction in equation. resulting Modified Kinetic Equation (MMKE) proved to warrant at same time condition mass-density incompressibility validity fluid In addition, it shown that conservation Boltzmann-Shannon entropy can similarly be warranted. Applications plane Couette Poiseuille flows are considered showing they regarded as final decaying states non-stationary flows. As result, arbitrary initial stochastic 1-body PDF evolving means MMKE necessarily exhibits phenomenon Decay Equilibrium (DKE), whereby asymptotically relaxes stationary spatially uniform Maxwellian PDF.

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