Global Solutions of the Boltzmann Equation over ${\mathbb{R}}^D$ near Global Maxwellians with Small Mass

We study the dynamics defined by the Boltzmann equation set in the Euclidean space ${\mathbb{R}}^D$ in the vicinity of global Maxwellians with finite mass. A global Maxwellian is a special solution of the Boltzmann equation for which the collision integral vanishes identically. In this setting, the dispersion due to the advection operator quenches the dissipative effect of the Boltzmann collision integral. As a result, the large time limit of solutions of the Boltzmann equation in this regime is given by noninteracting, freely transported states and can be described with the tools of scattering theory.