Boltzmann–Grad asymptotic behavior of collisional dynamics

DOI10.1142/S0129055X21300016zbMath1471.82008arXiv2001.06786MaRDI QIDQ5156030

Igor V. Gapyak, Viktor Gerasimenko

Publication date: 14 October 2021

Published in: Reviews in Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2001.06786

zbMATH Keywords

Boltzmann equationEnskog equationhard sphere dynamicsdual BBGKY hierarchyBoltzmann-Grad scaling

Mathematics Subject Classification ID

Kinetic theory of gases in time-dependent statistical mechanics (82C40) Classical dynamic and nonequilibrium statistical mechanics (general) (82C05) Nonlinear evolution equations (47J35) Boltzmann equations (35Q20) Applications of functional analysis in statistical physics (46N55)

Related Items (4)

Cluster expansion for a dilute hard sphere gas dynamics ⋮ Propagation of correlations in a hard-sphere system ⋮ Long‐time correlations for a hard‐sphere gas at equilibrium ⋮ Long-time derivation at equilibrium of the fluctuating Boltzmann equation

Cites Work

• From Newton to Boltzmann: hard spheres and short-range potentials
• Propagation of chaos and effective equations in kinetic theory: a brief survey
• The Boltzmann-Grad limit of a hard sphere system: analysis of the correlation error
• Heisenberg picture of quantum kinetic evolution in mean-field limit
• The propagation of chaos for a rarefied gas of hard spheres in the whole space
• Mathematics of granular materials
• Dynamical systems II. Ergodic theory with applications to dynamical systems and statistical mechanics. Transl. from the Russian
• The mathematical theory of dilute gases
• Low-density asymptotic behavior of observables of hard sphere fluids
• Kinetic and hydrodynamic models of nearly elastic granular flows
• Hard sphere dynamics and the Enskog equation
• Functionals for the means of observables for one-dimensional infinite-particle systems
• Microscopic and soliton-like solutions of the Boltzmann-Enskog and generalized Enskog equations for elastic and inelastic hard spheres
• Evolution of correlation functions in the hard sphere dynamics
• Derivation of the Boltzmann Equation: Hard Spheres, Short-Range Potentials and Beyond
• On the evolution of the empirical measure for the Hard-Sphere dynamics
• A mathematical description of the evolution of the state of infinite systems of classical statistical mechanics
• On Semigroups of Large Particle Systems and Their Scaling Asymptotic Behavior
• On the Boltzmann equation for rigid spheres
• Time evolution of large classical systems
• From Newton to Navier–Stokes, or how to connect fluid mechanics equations from microscopic to macroscopic scales
• Structure of correlations for the Boltzmann-Grad limit of hard spheres
• On the structure of expansions for the BBGKY hierarchy solutions
• Backward clusters, hierarchy and wild sums for a hard sphere system in a low-density regime
• The Boltzmann kinetic equation with correlations for hard sphere fluids
• On the non-Markovian Enskog equation for granular gases
• On the validity of the Boltzmann equation for short range potentials
• One-sided convergence in the Boltzmann–Grad limit
• Approaches to Derivation of the Boltzmann Equation with Hard Sphere Collisions
• The Boltzmann-Grad limit and Cauchy-Kovalevskaya theorem
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item

This page was built for publication: Boltzmann–Grad asymptotic behavior of collisional dynamics