Time-asymptotic expansion and fluid approximation of the 1D Boltzmann equation with hard potentials
Abstract
We establish a quantitative large-time comparison between the macroscopic Boltzmann solution and the full nonlinear compressible Navier-Stokes solution in one space dimension. For Maxwellian molecules and hard potentials with angular cutoff, we consider small, spatially compactly supported perturbations of a global Maxwellian with polynomial velocity decay, without assuming spatial differentiability. Nonlinear diffusion waves persist at leading order, making comparison through linearized equations alone insufficient. We construct a coupled system for the leading nonlinear fluid waves and derive cancellation identities from the exact kinetic spectral representation to control interactions between distinct characteristic families. Combined with a particle-fluid decomposition, these yield pointwise estimates separating the leading waves, their interactions, and a faster-decaying remainder.
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BibTeX
@misc{chang2026timeasymptotic,
title = {{Time-asymptotic expansion and fluid approximation of the 1D Boltzmann equation with hard potentials}},
author = {Hui-Tzu Chang and Haitao Wang and Kung-Chien Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.34174},
eprint = {2610.34174},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.34174},
}
RIS
TY - UNPB
TI - Time-asymptotic expansion and fluid approximation of the 1D Boltzmann equation with hard potentials
AU - Hui-Tzu Chang
AU - Haitao Wang
AU - Kung-Chien Wu
PY - 2026
DA - 2026/10/25
PB - arXiv
DO - 10.48550/arxiv.2610.34174
UR - https://arxiv.org/abs/2610.34174
AB - We establish a quantitative large-time comparison between the macroscopic Boltzmann solution and the full nonlinear compressible Navier-Stokes solution in one space dimension. For Maxwellian molecules and hard potentials with angular cutoff, we consider small, spatially compactly supported perturbations of a global Maxwellian with polynomial velocity decay, without assuming spatial differentiability. Nonlinear diffusion waves persist at leading order, making comparison through linearized equations alone insufficient. We construct a coupled system for the leading nonlinear fluid waves and derive cancellation identities from the exact kinetic spectral representation to control interactions between distinct characteristic families. Combined with a particle-fluid decomposition, these yield pointwise estimates separating the leading waves, their interactions, and a faster-decaying remainder.
ER -