L²-Stability theory of the Boltzmann equation near a global Maxwellian

We present three a priori L²-stability estimates for classical solutions to the Boltzmann equation with a cut-off inverse power law potential, when initial datum is a perturbation of a global Maxwellian. We show that L²-stability estimates of classical solutions depend on Strichartz type estimates of perturbations and the non-positive definiteness of the linearized collision operator. Several well known classical solutions to the Boltzmann equation fit our L²-stability framework.