English

Velocity Decay Estimates for Boltzmann equation with hard potentials

Analysis of PDEs 2020-06-24 v1

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+2s>2\gamma +2s > 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-Mouhot-Silvestre (arXiv:1804.06135), which addressed the case of moderately soft potentials (γ+2s[0,2]\gamma + 2s \in [0,2]).

Keywords

Cite

@article{arxiv.1910.01613,
  title  = {Velocity Decay Estimates for Boltzmann equation with hard potentials},
  author = {Stephen Cameron and Stanley Snelson},
  journal= {arXiv preprint arXiv:1910.01613},
  year   = {2020}
}

Comments

16 pages

R2 v1 2026-06-23T11:34:00.492Z