A gradient flow approach to the Boltzmann equation

Interacting random processes; statistical mechanics type models; percolation theory (60K35) PDEs with randomness, stochastic partial differential equations (35R60) Kinetic theory of gases in time-dependent statistical mechanics (82C40) Boltzmann equations (35Q20)

Cites Work

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A consistency estimate for Kac's model of elastic collisions in a dilute gas
Kac's program in kinetic theory
Gradient flows of the entropy for jump processes
Well-posedness of Lagrangian flows and continuity equations in metric measure spaces
On the relation between gradient flows and the large-deviation principle, with applications to Markov chains and diffusion
Quantitative and qualitative Kac's chaos on the Boltzmann's sphere
Propagation of chaos for the Landau equation with moderately soft potentials
Gradient flows of the entropy for finite Markov chains
A new class of transport distances between measures
Strict entropy production bounds and stability of the rate of convergence to equilibrium for the Boltzmann equation
On the spatially homogeneous Boltzmann equation
Quantitative uniform propagation of chaos for Maxwell molecules
Quantitative estimates of propagation of chaos for stochastic systems with \(W^{-1,\infty}\) kernels
Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation
Conservation of energy, entropy identity, and local stability for the spatially homogeneous Boltzmann equation
A computational fluid mechanics solution to the Monge-Kantorovich mass transfer problem
Large deviations for Kac-like walks
Jump processes as generalized gradient flows
On Kac's chaos and related problems
On the Boltzmann equation. I: Existence
THE GEOMETRY OF DISSIPATIVE EVOLUTION EQUATIONS: THE POROUS MEDIUM EQUATION
From a Kac-like particle system to the Landau equation for hard potentials and Maxwell molecules
A gradient structure for reaction–diffusion systems and for energy-drift-diffusion systems
[https://portal.mardi4nfdi.de/wiki/Publication:3347061 �quations de type de Boltzmann, spatialement homog�nes]
A Γ-convergence approach to large deviations
Gamma-convergence of gradient flows with applications to Ginzburg-Landau
A gradient flow approach to linear Boltzmann equations
Optimal Transport

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