Microscopic statistical description of incompressible Navier-Stokes granular fluids

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F47813059%3A19240%2F17%3AA0000018" target="_blank" >RIV/47813059:19240/17:A0000018 - isvavai.cz</a>
Result on the web
<a href="https://link.springer.com/article/10.1140%2Fepjp%2Fi2017-11472-2" target="_blank" >https://link.springer.com/article/10.1140%2Fepjp%2Fi2017-11472-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1140/epjp/i2017-11472-2" target="_blank" >10.1140/epjp/i2017-11472-2</a>

Result language
angličtina
Original language name
Microscopic statistical description of incompressible Navier-Stokes granular fluids
Original language description
Based on the recently established Master kinetic equation and related Master constant H-theorem which describe the statistical behavior of the Boltzmann-Sinai classical dynamical system for smooth and hard spherical particles, the problem is posed of determining a microscopic statistical description holding for an incompressible Navier-Stokes fluid. The goal is reached by introducing a suitable mean-field interaction in the Master kinetic equation. The resulting Modified Master Kinetic Equation (MMKE) is proved to warrant at the same time the condition of mass-density incompressibility and the validity of the Navier-Stokes fluid equation. In addition, it is shown that the conservation of the Boltzmann-Shannon entropy can similarly be warranted. Applications to the plane Couette and Poiseuille flows are considered showing that they can be regarded as final decaying states for suitable non-stationary flows. As a result, it is shown that an arbitrary initial stochastic 1-body PDF evolving in time by means of MMKE necessarily exhibits the phenomenon of Decay to Kinetic Equilibrium (DKE), whereby the same 1-body PDF asymptotically relaxes to a stationary and spatially uniform Maxwellian PDF.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10305 - Fluids and plasma physics (including surface physics)

Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)<br>I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2017
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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