PreprintarXiv licencearXiv
Optimal time decay of the Boltzmann equation with cutoff soft potentials in the whole space
Abstract
Since Strain's work \cite{Strain-2012-KRM} on almost optimal time decay rates for the microscopic part of perturbative classical solutions to the Boltzmann system with soft potentials via the time-velocity splitting method, how to obtain the optimal decay of the microscopic part has remained unsolved. In this paper, we resolve this problem by developing a nonlinear energy estimate method different from the time-velocity splitting approach. The proof relies on a combination of a hierarchy of time-weighted energy estimates, the damping factor e−ν(v)(t−τ), and a dyadic decomposition of velocity space.
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BibTeX
@misc{lei2026optimal,
title = {{Optimal time decay of the Boltzmann equation with cutoff soft potentials in the whole space}},
author = {Yuanjie Lei and Xiongju Wei and Tong Yang and Huijiang Zhao},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.32296},
eprint = {2610.32296},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.32296},
}
RIS
TY - UNPB
TI - Optimal time decay of the Boltzmann equation with cutoff soft potentials in the whole space
AU - Yuanjie Lei
AU - Xiongju Wei
AU - Tong Yang
AU - Huijiang Zhao
PY - 2026
DA - 2026/10/23
PB - arXiv
DO - 10.48550/arxiv.2610.32296
UR - https://arxiv.org/abs/2610.32296
AB - Since Strain's work \cite{Strain-2012-KRM} on almost optimal time decay rates for the microscopic part of perturbative classical solutions to the Boltzmann system with soft potentials via the time-velocity splitting method, how to obtain the optimal decay of the microscopic part has remained unsolved. In this paper, we resolve this problem by developing a nonlinear energy estimate method different from the time-velocity splitting approach. The proof relies on a combination of a hierarchy of time-weighted energy estimates, the damping factor e^−ν(v)(t−τ), and a dyadic decomposition of velocity space.
ER -