Global wellposedness of a binary–ternary Boltzmann equation
Abstract
In this paper we show global wellposedness near vacuum for the binaryternary Boltzmann equation. The binaryternary Boltzmann equation provides a correction term to the classical Boltzmann equation, taking into account both binary and ternary interactions of particles, and may serve as a more accurate description model for denser gases in nonequilibrium. Wellposedness of the classical Boltzmann equation and, independently, the purely ternary Boltzmann equation follow as special cases. To prove global wellposedness, we use a KanielShinbrot iteration and related work to approximate the solution of the nonlinear equation by monotone sequences of supersolutions and subsolutions. This analysis required establishing new convolution type estimates to control the contribution of the ternary collisional operator to the model. We show that the ternary operator allows consideration of softer potentials than the one binary operator, consequently our solution to the ternary correction of the Boltzmann equation preserves all the properties of the binary interactions solution. These results are novel for collisional operators of monoatomic gases with either hard or soft potentials that model both binary and ternary interactions.
 Publication:

Annales de L'Institut Henri Poincare Section (C) Non Linear Analysis
 Pub Date:
 February 2022
 DOI:
 10.4171/aihpc/9
 arXiv:
 arXiv:1910.14476
 Bibcode:
 2022AIHPC..39..327A
 Keywords:

 Mathematics  Analysis of PDEs;
 Mathematical Physics
 EPrint:
 accepted in Ann. Inst. H. Poincar\'e Anal. Non Lin\'eaire, 35 pages