A stochastic particle numerical method for 3D Boltzmann equations without cutoff

DOI10.1090/S0025-5718-01-01339-4zbMath0990.60085OpenAlexW1995125414MaRDI QIDQ2781211

Sylvie Méléard, Nicolas Fournier

Publication date: 19 March 2002

Published in: Mathematics of Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0025-5718-01-01339-4

zbMATH Keywords

stochastic differential equationsinteracting particle systemsjump measuresBoltzmann equations without cutoff

Mathematics Subject Classification ID

Related Items (20)

Rate of convergence of the Nanbu particle system for hard potentials and Maxwell molecules ⋮ The multifractal nature of Boltzmann processes ⋮ Kac's process with hard potentials and a moderate angular singularity ⋮ Uniqueness and propagation of chaos for the Boltzmann equation with moderately soft potentials ⋮ On the well-posedness of the spatially homogeneous Boltzmann equation with a moderate angular singularity ⋮ White-noise driven conditional McKean-Vlasov limits for systems of particles with simultaneous and random jumps ⋮ Uniqueness for a class of spatially homogeneous Boltzmann equations without angular cutoff ⋮ Kac's program in kinetic theory ⋮ Construction of Boltzmann and McKean-Vlasov type flows (the sewing lemma approach) ⋮ A Feynman-Kac-type formula for the deterministic and stochastic wave equations and other p.d.e.'s ⋮ About Kac's program in kinetic theory ⋮ On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity ⋮ On exponential moments of the homogeneous Boltzmann equation for hard potentials without cutoff ⋮ Quantitative uniform propagation of chaos for Maxwell molecules ⋮ Brownian approximation and Monte Carlo simulation of the non-cutoff Kac equation ⋮ Pointwise convergence of Boltzmann solutions for grazing collisions in a Maxwell gas via a probabilitistic interpretation ⋮ A recursive algorithm and a series expansion related to the homogeneous Boltzmann equation for hard potentials with angular cutoff ⋮ Propagation of chaos: a review of models, methods and applications. II: Applications ⋮ Finiteness of entropy for the homogeneous Boltzmann equation with measure initial condition ⋮ Kac's chaos and Kac's program

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• A Convergence Proof for Nanbu’s Simulation Method for the Full Boltzmann Equation
• Probabilistic treatment of the Boltzmann equation of Maxwellian molecules
• Convergence of the fluctuations for interacting diffusions with jumps associated with boltzmann equations

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