Moment estimates for polyatomic Boltzmann equation with frozen collisions

TL;DR

This paper derives moment estimates for the polyatomic Boltzmann equation with frozen collisions, analyzing energy conservation and combining results for different collision types to understand moment generation and propagation.

Contribution

It introduces new a priori moment estimates for solutions with frozen collisions and integrates these with existing results for pure polyatomic collisions.

Findings

Moment generation is driven by the pure polyatomic collision operator.

Moment propagation property is established for the combined collision model.

Analysis covers both frozen and pure polyatomic collision regimes.

Abstract

In this paper, a polyatomic gas with continuous internal energy is considered, allowing for frozen collisions, in which the kinetic energy of the colliding particle pair is conserved, and the internal energy of each particle remains unchanged. A priori moment estimates are derived for solutions of the space-homogeneous Boltzmann equation with a collision kernel of the hard potentials type with cut-off. The model with frozen collisions is first analyzed, followed by a review of general collisions--referred to as pure polyatomic--which preserve the total kinetic and internal energy. By combining existing results for pure polyatomic collisions with the newly derived estimates for frozen collisions, moment estimates are established for the Boltzmann equation with a collision operator that convexly combines both types of collisions. In particular, the moment generation property is shown to be driven by the rate of the pure polyatomic operator, and the moment propagation property holds.