2006/11/12 by Massimo Tessarotto, Tessarotto, Massimo, Marco Ellero +1 · 2 citations
Mathematics · Medicine · Physics and Astronomy · #Advanced Thermodynamics and Statistical Mechanics #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Fluid Dynamics (physics.flu-dyn) #Gas Dynamics and Kinetic Theory #Thermoregulation and physiological responses #physics.comp-ph #physics.flu-dyn
paper · pdf · doi:10.48550/arxiv.physics/0611113
Communication presented at the 25th International Symposium on Rarefied Gas Dynamics, St. Petersburg, Russia, July 21-28, 2006
arxiv created 2006/11/12 · openalex publication_date 2006/11/12 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Fundamental aspects of inverse kinetic theories for incompressible Navier-Stokes equations concern the possibility of defining uniquely the kinetic equation underlying such models and furthermore, the construction of a kinetic theory implying also the energy equation. The latter condition is consistent with the requirement that fluid fields result classical solutions of the fluid equations. These issues appear of potential relevance both from the mathematical viewpoint and for the physical interpretation of the theory. In this paper we intend to prove that the non-uniqueness feature can be resolved by imposing suitable assumptions. These include, in particular, the requirement that the kinetic equation be equivalent, in a suitable sense, to a Fokker-Planck kinetic equation. Its Fokker-Planck coefficients are proven to be uniquely determined by means of appropriate prescriptions. In addition, as a further result, it is proven that the inverse kinetic equation satisfies both an entropy principle and the energy equation for the fluid fields.