Moment estimates and well-posedness of the binary-ternary Boltzmann equation

TL;DR

This paper establishes moment generation and propagation, along with global well-posedness, for the homogeneous binary-ternary Boltzmann equation, highlighting improved properties due to combined binary and ternary collisions.

Contribution

It introduces angular averaging estimates for ternary interactions and demonstrates enhanced moment generation and decay in the combined binary-ternary setting.

Findings

Binary-ternary collisions improve moment generation.

Combined collisions lead to better time decay.

First development of angular averaging estimates for ternary interactions.

Abstract

In this paper, we show generation and propagation of polynomial and exponential moments, as well as global well-posedness of the homogeneous binary-ternary Boltzmann equation. We also show that the co-existence of binary and ternary collisions yields better generation properties and time decay, than when only binary or ternary collisions are considered. To address these questions, we develop for the first time angular averaging estimates for ternary interactions. This is the first paper which discusses this type of questions for the binary-ternary Boltzmann equation and opens the door for studying moments properties of gases with higher collisional density.