Rigorous derivation of a binary-ternary Boltzmann equation for a hard-sphere gas

Rigorous derivation of a binary-ternary Boltzmann equation for a hard-sphere gas

-
Ioakeim Ampatzoglou, New York University

Zoom link: https://princeton.zoom.us/j/4745473988

In this talk, we will focus on the rigorous derivation of a binary-ternary Boltzmann equation describing the kinetic properties of a dense hard-spheres gas, where particles undergo either binary or ternary instantaneous interactions, while preserving momentum and energy. An important challenge in deriving this equation is related to providing a mathematical framework allowing to detect both binary and ternary interactions. To achieve that, we introduced new algebraic and geometric techniques in order to eventually decouple binary and ternary interactions and understand the way they could succeed one another in time.