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Relative Entropy Method for Particle Approximation of the Landau Equation for Maxwellian Molecules

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arxiv 2408.15035 v2 pith:HAR5U6VA submitted 2024-08-27 math.AP math.PR

José Antonio Carrillo , Xuanrui Feng , Shuchen Guo , Pierre-Emmanuel Jabin , Zhenfu Wang This is my paper · ORCID
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We derive the spatially homogeneous Landau equation for Maxwellian molecules from a natural stochastic interacting particle system. More precisely, we control the relative entropy between the joint law of the particle system and the tensorized law of the Landau equation. To obtain this, we establish as key tools the pointwise logarithmic gradient and Hessian estimates of the density function and also a new Law of Large Numbers result for the particle system. The logarithmic estimates are derived via the Bernstein method and the parabolic maximum principle, while the Law of Large Numbers result comes from crucial observations on the control of moments at the particle level.

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Cited by 5 Pith papers

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  1. Kac's Program for the Landau Equation

    math.AP 2025-06 conditional novelty 8.0 of 10

    The k-particle velocity marginals of Kac's particle system converge to the factorized law of the Landau solution for all power-law potentials, including Coulomb collisions, in weak, Wasserstein, entropic, and strong L...

  2. Propagation of chaos for multi-species moderately interacting particle systems up to Newtonian singularity

    math.PR 2025-01 accept novelty 8.0 of 10

    Multi-species moderately interacting particle systems converge in L1 to aggregation-diffusion PDEs with Coulomb-singular kernels at an algebraic rate in the particle number.

  3. Weak-strong uniqueness for the Landau equation by a relative entropy method

    math.AP 2025-05 accept novelty 7.0 of 10

    For the Landau equation with soft potentials (including Coulomb), this paper proves that all H-solutions with enough moments coincide with the smooth solution, via a relative entropy estimate.

  4. The fluctuation behaviour of the stochastic point vortex model with common noise

    math.PR 2025-01 conditional novelty 6.0 of 10

    The fluctuation process of the stochastic point vortex model with common noise converges in distribution to the unique strong solution of a linear fluctuation SPDE with multiplicative transport noise and a conditional...

  5. A structure-preserving collisional particle method for the Landau kinetic equation

    math.NA 2024-12 conditional novelty 6.0 of 10

    An exact spherical-Brownian-motion time discretization of a paired collisional particle system gives a structure-preserving O(N) stochastic method for the Landau equation.

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