Velocity decay estimates for Boltzmann equation with hard potentials. (4th May 2020)

• Record Type: Journal Article
• Authors: Cameron, Stephen; Snelson, Stanley
• Is Part Of: Nonlinearity. Volume 33:Number 6(2020)
• Page Start: 2941
• Page End: 2958
• Publication Date: 2020-05-04
• Subjects: Boltzmann equation -- kinetic theory -- decay estimates; 35Q82, 76P05, 35Q20; Nonlinear theories -- Periodicals; Mathematical analysis -- Periodicals; Mathematical analysis; Nonlinear theories; Periodicals; 515
• DOI: 10.1088/1361-6544/ab7729
• Languages: English
• ISSNs: 0951-7715

Abstract

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]).