DOI10.4171/129zbMath1315.82001arXiv1208.5753OpenAlexW1501394657MaRDI QIDQ389927
Laure Saint-Raymond, Benjamin Texier, Isabelle Gallagher
Publication date: 22 January 2014
Published in: Zurich Lectures in Advanced Mathematics (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/1208.5753
A Microscopic Point of View on Singularities in Fluid Models ⋮
Reduced fluctuations for bosons in a double well ⋮
Irreversibility in the derivation of the Boltzmann equation ⋮
Asymptotic-preserving schemes for multiscale physical problems ⋮
A kinetic model for epidemic spread ⋮
Low-density asymptotic behavior of observables of hard sphere fluids ⋮
Continuum and thermodynamic limits for a simple random-exchange model ⋮
On the Cauchy problem for the homogeneous Boltzmann-Nordheim equation for bosons: local existence, uniqueness and creation of moments ⋮
Projective and telescopic projective integration for non-linear kinetic mixtures ⋮
On Semigroups of Large Particle Systems and Their Scaling Asymptotic Behavior ⋮
Asymptotic stability of the Boltzmann equation with Maxwell boundary conditions ⋮
Derivation of an Ornstein-Uhlenbeck process for a massive particle in a rarified gas of particles ⋮
The Boltzmann equation for a multi-species mixture close to global equilibrium ⋮
A Rigorous Derivation of a Boltzmann System for a Mixture of Hard-Sphere Gases ⋮
Propagation of correlations in a hard-sphere system ⋮
From Newton to Navier–Stokes, or how to connect fluid mechanics equations from microscopic to macroscopic scales ⋮
Derivation of a non-autonomous linear Boltzmann equation from a heterogeneous Rayleigh gas ⋮
From hard sphere dynamics to the Stokes-Fourier equations: an \(L^2\) analysis of the Boltzmann-Grad limit ⋮
From a non-Markovian system to the Landau equation ⋮
Stability of the Maxwell-Stefan system in the diffusion asymptotics of the Boltzmann multi-species equation ⋮
The derivation of the linear Boltzmann equation from a Rayleigh gas particle model ⋮
Uniqueness of solutions to the spectral hierarchy in kinetic wave turbulence theory ⋮
Local well-posedness for Boltzmann's equation and the Boltzmann hierarchy via Wigner transform ⋮
On the weak coupling limit of quantum many-body dynamics and the quantum Boltzmann equation ⋮
A kinetic equation for the distribution of interaction clusters in rarefied gases ⋮
Propagation of chaos for the spatially homogeneous Landau equation for Maxwellian molecules ⋮
A Kac model for kinetic annihilation ⋮
About Lanford's theorem in the half-space with specular reflection ⋮
The grazing collisions limit from the linearized Boltzmann equation to the Landau equation for short-range potentials ⋮
Full derivation of the wave kinetic equation ⋮
Dynamics of dilute gases: a statistical approach ⋮
Long-time derivation at equilibrium of the fluctuating Boltzmann equation ⋮
The derivation of the compressible Euler equation from quantum many-body dynamics ⋮
Fluctuation theory in the Boltzmann-Grad limit ⋮
Bosons in a double well: two-mode approximation and fluctuations ⋮
Hypocoercivity for perturbation theory and perturbation of hypocoercivity for confined Boltzmann-type collisional equations ⋮
Structure of correlations for the Boltzmann-Grad limit of hard spheres ⋮
On the dynamics of dilute gases ⋮
The compressible Euler and acoustic limits from quantum Boltzmann equation with Fermi-Dirac statistics ⋮
Dynamical large deviations for an inhomogeneous wave kinetic theory: linear wave scattering by a random medium ⋮
Is the Boltzmann equation reversible? A large deviation perspective on the irreversibility paradox ⋮
The BGK equation as the limit of an \(N\)-particle system ⋮
Vanishing angular singularity limit to the hard-sphere Boltzmann equation ⋮
Typicality, irreversibility and the status of macroscopic laws ⋮
On the emergence of quantum Boltzmann fluctuation dynamics near a Bose-Einstein condensate ⋮
From Boltzmann to incompressible Navier–Stokes in Sobolev spaces with polynomial weight ⋮
The rigorous derivation of the linear Landau equation from a particle system in a weak-coupling limit ⋮
Microscopic solutions of the Boltzmann-Enskog equation in the series representation ⋮
Linear diffusive limit of deterministic systems of hard spheres ⋮
Microscopic solutions of kinetic equations and the irreversibility problem ⋮
Rigorous derivation of a ternary Boltzmann equation for a classical system of particles ⋮
From the Boltzmann equation to the incompressible Navier-Stokes equations on the torus: a quantitative error estimate ⋮
Interacting particle systems with long-range interactions: scaling limits and kinetic equations ⋮
Boltzmann–Grad asymptotic behavior of collisional dynamics ⋮
Chaotic distributions for relativistic particles ⋮
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 ⋮
Hilbert’s 6th Problem: exact and approximate hydrodynamic manifolds for kinetic equations ⋮
A mathematical PDE perspective on the Chapman–Enskog expansion ⋮
Kinetic theory of cluster dynamics ⋮
One-sided convergence in the Boltzmann–Grad limit ⋮
On the growth of a particle coalescing in a Poisson distribution of obstacles ⋮
Phase transitions and macroscopic limits in a BGK model of body-attitude coordination ⋮
Turbulent energy spectrum via an interaction potential ⋮
On the Boltzmann equation with stochastic kinetic transport: global existence of renormalized martingale solutions ⋮
The propagation of chaos for a rarefied gas of hard spheres in the whole space ⋮
On the cardinality of collisional clusters for hard spheres at low density ⋮
Scaling limits of bosonic ground states, from many-body to non-linear Schrödinger ⋮
The relativistic quantum Boltzmann equation near equilibrium ⋮
Stability of global equilibrium for the multi-species Boltzmann equation in \(L^\infty\) settings ⋮
Perturbative theory for the Boltzmann equation in bounded domains with different boundary conditions ⋮
Evolution of correlation functions in the hard sphere dynamics ⋮
Quantitative estimates of propagation of chaos for stochastic systems with \(W^{-1,\infty}\) kernels ⋮
Continuum thermodynamics of chemically reacting fluid mixtures ⋮
Onset of the wave turbulence description of the longtime behavior of the nonlinear Schrödinger equation ⋮
On the kinetic wave turbulence description for NLS ⋮
On the homogenization of the Stokes equations in perforated domains with application to fluid/solid interaction problems ⋮
The incompressible Navier-Stokes-Fourier limit from Boltzmann-Fermi-Dirac equation ⋮
Derivation of the Boltzmann Equation: Hard Spheres, Short-Range Potentials and Beyond ⋮
Multiscale sparse microcanonical models ⋮
Virial estimates for hard spheres ⋮
A derivation of the Liouville equation for hard particle dynamics with non-conservative interactions ⋮
Boltzmann-Grad limit of a hard sphere system in a box with isotropic boundary conditions ⋮
Propagation of chaos for topological interactions ⋮
The Boltzmann-Grad limit for the Lorentz gas with a Poisson distribution of obstacles ⋮
Propagation of chaos: a review of models, methods and applications. I: Models and methods ⋮
Propagation of chaos: a review of models, methods and applications. II: Applications ⋮
On the derivation of the wave kinetic equation for NLS ⋮
Diffusive Limit for the Random Lorentz Gas ⋮
A Kac model for fermions ⋮
Graphon Mean Field Games and Their Equations ⋮
A review of the mean field limits for Vlasov equations ⋮
Exponential approach to, and properties of, a non-equilibrium steady state in a dilute gas ⋮
On the transfer of energy towards infinity in the theory of weak turbulence for the nonlinear Schrödinger equation ⋮
New approach to derivation of quantum kinetic equations with initial correlations
This page was built for publication: From Newton to Boltzmann: hard spheres and short-range potentials