Rigorous derivation of a ternary Boltzmann equation for a classical system of particles

Abstract

In this paper, we present a rigorous derivation of a new kinetic equation describing the limiting behavior of a classical system of particles with three particle elastic instantaneous interactions, which are modeled using a non-symmetric version of a ternary distance. The ternary collisional operator we derive can be seen as the first step towards obtaining a toy model for a non-ideal gas where higher order interactions are taken into account.

accepted in Comm. Math. Phys. 49 pages. arXiv admin note: text overlap with arXiv:2007.00446

References in corpus (5)

• Three-body interactions in colloidal systems
• The propagation of chaos for a rarefied gas of hard spheres in the whole space
• Global well-posedness of a binary-ternary Boltzmann equation
• Rigorous derivation of a ternary Boltzmann equation for a classical system of particles
• Rigorous derivation of a binary-ternary Boltzmann equation for a dense gas of hard spheres

Cited by in corpus (6)

• Global well-posedness of a binary-ternary Boltzmann equation
• Rigorous derivation of a ternary Boltzmann equation for a classical system of particles
• Uniqueness of Solutions to the Spectral Hierarchy in Kinetic Wave Turbulence Theory
• Rigorous derivation of a binary-ternary Boltzmann equation for a dense gas of hard spheres
• Moment estimates and well-posedness of the binary-ternary Boltzmann equation
• On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein Condensate