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Abstract In this paper we describe the long‐time behavior of the non‐cutoff Boltzmann equation with soft potentials near a global Maxwellian background on the whole space in the weakly collisional limit (that is, infinite Knudsen number ). Specifically, we prove that for initial data sufficiently small (independent of the Knudsen number), the solution displays several dynamics caused by the phase mixing/dispersive effects of the transport operator and its interplay with the singular collision operator. For ‐wavenumbers with , one sees anenhanced dissipationeffect wherein the characteristic decay time‐scale is accelerated to , where is the singularity of the kernel ( being the Landau collision operator, which is also included in our analysis); for , one seesTaylor dispersion, wherein the decay time‐scale is accelerated to . Additionally, we prove almost uniform phase mixing estimates. For macroscopic quantities such as the density , these bounds imply almost uniform‐in‐ decay of in due to phase mixing and dispersive decay.
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This content will become publicly available on August 2, 2026
Fast spectral separation method for kinetic equation with anisotropic non-stationary collision operator retaining micro-model fidelity
In this paper, we present a generalized, data-driven collisional operator for one-component plasmas, learned from molecular dynamics simulations, to extend the collisional kinetic model beyond the weakly coupled regime. The proposed operator features an anisotropic, non-stationary collision kernel that accounts for particle correlations typically neglected in classical Landau formulations. To enable efficient numerical evaluation, we develop a fast spectral separation method that represents the kernel as a low-rank tensor product of univariate basis functions. This formulation admits an O(N log N) algorithm via fast Fourier transforms and preserves key physical properties, including discrete conservation laws and the H-theorem, through a structure-preserving central difference discretization. Numerical experiments demonstrate that the proposed model accurately captures plasma dynamics in the moderately coupled regime beyond the standard Landau model while maintaining high computational efficiency and structure-preserving properties.
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- Award ID(s):
- 2110981
- PAR ID:
- 10633351
- Publisher / Repository:
- arxiv
- Date Published:
- Journal Name:
- arXivorg
- ISSN:
- 2331-8422
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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