From hard sphere dynamics to the Stokes-Fourier equations: an \(L^2\) analysis of the Boltzmann-Grad limit

DOI10.1007/s40818-016-0018-0zbMath1403.35194OpenAlexW2130650797MaRDI QIDQ1661394

Thierry Bodineau, Isabelle Gallagher, Laure Saint-Raymond

Publication date: 16 August 2018

Published in: Annals of PDE (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s40818-016-0018-0

zbMATH Keywords

symmetrycumulant expansionfluid limitshard sphere dynamicsStokes-Fourier equationsweak chaos property

Mathematics Subject Classification ID

Related Items (27)

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Cites Work

• Unnamed Item
• Unnamed Item
• From Newton to Boltzmann: hard spheres and short-range potentials
• From Newton's law to the linear Boltzmann equation without cut-off
• The Boltzmann-Grad limit of a hard sphere system: analysis of the correlation error
• On the Cauchy problem for Boltzmann equations: Global existence and weak stability
• The incompressible Navier-Stokes limit of the Boltzmann equation for hard cutoff potentials
• Derivation of the Boltzmann equation from particle dynamics
• The mathematical theory of dilute gases
• Boltzmann equation: micro-macro decompositions and positivity of shock profiles
• Equilibrium time correlation functions in the low-density limit
• Equilibrium fluctuations for the discrete Boltzmann equation
• Linear diffusive limit of deterministic systems of hard spheres
• Evolution of correlation functions in the hard sphere dynamics
• Symmetric Measures on Cartesian Products
• The fluid dynamic limit of the nonlinear boltzmann equation
• On the existence of global solutions of mixed problem for non-linear Boltzmann equation
• Time evolution of large classical systems
• Fluid dynamic limits of kinetic equations II convergence proofs for the boltzmann equation
• Stokes-Fourier and acoustic limits for the Boltzmann equation: Convergence proofs
• The Boltzmann equation in the whole space
• On the validity of the Boltzmann equation for short range potentials

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