Work

Time-asymptotic expansion and fluid approximation of the 1D Boltzmann equation with hard potentials

Year: 2026

Type: preprint

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.

Source: arXiv (Cornell University)

DOI: 10.48550/arxiv.2610.34174

Authors: Chang, Hui-Tzu, Wang, Haitao, Wu, Kung-Chien

Institutions: National Taiwan University, National Center for Theoretical Sciences, Shanghai Jiao Tong University, National Cheng Kung University

Language: English

Topic: Gas Dynamics and Kinetic Theory

Subfield: Applied Mathematics

Field: Mathematics

Domain: Physical Sciences

Open Access status: green

Funders: National Center for Theoretical Sciences, National Natural Science Foundation of China, National Science and Technology Council

Awards: G3942283580, G7627071985

OpenAlex ID: W7223811816

Cites: 1

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Related to: 10