Long‐Time Validity of the Linearized Boltzmann Uncut‐Off and the Linearized Landau Equations From the Newton Law
Abstract
ABSTRACT We provide a rigorous justification of the linearized Boltzmann and Landau equations for interacting particle systems with long‐range interaction. The result shows that for a system of Hamiltonian particles governed by truncated power law potentials of the form near (with the effective radius of the particles), the covariance of the equilibrium fluctuations converges to solutions of kinetic equations in appropriate scaling limits and , corresponding to a low density regime. We prove that in Dimension 3, for , the limiting system approaches the uncut‐off linearized Boltzmann equation for the scaling . The Coulomb singularity appears as a threshold value. Kinetic scaling limits with universally converge to the linearized Landau equation, and we prove the onset of the Coulomb logarithm for .
Fields of Study & Subjects
Gas Dynamics and Kinetic Theory
Advanced Thermodynamics and Statistical Mechanics
Numerical methods in inverse problems
Publication details
- Journal / source
- Communications on Pure and Applied Mathematics
- Publisher
- Wiley
- Volume
- 79
- Issue
- 7
- Pages
- 1673–1745
- Publication date
- 20 February 2026
- Language
- EN