Moment estimates for polyatomic Boltzmann equation with frozen collisions

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.