Velocity decay estimates for Boltzmann equation with hard potentials. (4th May 2020) - Cameron, Stephen; Snelson, Stanley
Abstract: We establish pointwise polynomial decay estimates in velocity space for the spatially inhomogeneous Boltzmann equation without cutoff, in the case of hard potentials ( γ + 2 s > 2), under the assumption that the mass, energy, and entropy densities are bounded above, and the mass density is bounded below. These estimates are self-generating, i.e. they do not require corresponding decay assumptions on the initial data. Our results extend the recent work of Imbert et al [2020 J. École Polytech. 7 143–83], which addressed the case of moderately soft potentials ( γ + 2 s ∈ [0, 2]).