From Kac particles to the Landau equation with hard potentials: BBGKY hierarchy method

2025/08/14 by Guo, Shuchen
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2508.10697

Abstract

We study the Kac particle model for the space-homogenous Landau equation with hard potentials. By showing a sharper Povzner-type inequality, we obtain the uniform-in-time and uniform-in-N propagation of exponential moment for the first marginal of the solution of the many-particle Liouville equation. This key property enables us to show the uniqueness of weak solutions of the corresponding infinite Landau hierarchy by coupling method. As a result, we prove the propagation of chaos for the Landau equation with hard potentials.

Citations

• Kac's Program for the Landau Equation
• From Fisher information decay for the Kac model to the Landau-Coulomb hierarchy
• Rate of convergence of the Kac particle system for the Boltzmann equation with hard potentials
• Relative Entropy Method for Particle Approximation of the Landau Equation for Maxwellian Molecules
• Sharp local propagation of chaos for mean field particles with W^-1,∞ kernels
• On the global in time existence and uniqueness of solutions to the Boltzmann hierarchy
• The Derivation of the Boltzmann Equation from Quantum Many-body Dynamics
• The Landau equation does not blow up
• Entropic propagation of chaos for mean field diffusion with L^p interactions via hierarchy, linear growth and fractional noise
• Stability, well-posedness and regularity of the homogeneous Landau equation for hard potentials
• Local well-posedness for Boltzmann's equation and the Boltzmann hierarchy via Wigner transform
• Quantitative uniform propagation of chaos for Maxwell molecules
• From a Kac-like particle system to the Landau equation for hard potentials and Maxwell molecules
• Propagation of chaos for the Landau equation with moderately soft\n potentials
• Propagation of chaos for the spatially homogeneous Landau equation for Maxwellian molecules
• From Newton to Boltzmann: hard spheres and short-range potentials
• Kac's Program in Kinetic Theory
• Particle approximation of some Landau equations
• Measurability of optimal transportation and convergence rate for Landau type interacting particle systems
• Derivation of the Gross-Pitaevskii Hierarchy for the Dynamics of Bose-Einstein Condensate
• Derivation of the Gross-Pitaevskii Equation for the Dynamics of Bose-Einstein Condensate

Related

• Kac's Program for the Landau Equation
• From a Kac-like particle system to the Landau equation for hard potentials and Maxwell molecules
• From Fisher information decay for the Kac model to the Landau-Coulomb hierarchy
• Convergence to the Landau equation from the truncated BBGKY hierarchy in the weak-coupling limit
• Propagation of chaos for the Landau equation with moderately soft\n potentials