Uniqueness for a class of spatially homogeneous Boltzmann equations without angular cutoff

DOI10.1007/s10955-006-9208-6zbMath1107.82045OpenAlexW2123459108MaRDI QIDQ867701

Nicolas Fournier

Publication date: 16 February 2007

Published in: Journal of Statistical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s10955-006-9208-6

zbMATH Keywords

uniquenessBoltzmann equationWasserstein distance

Mathematics Subject Classification ID

Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Kinetic theory of gases in time-dependent statistical mechanics (82C40)

Related Items

Stability and uniqueness for the spatially homogeneous Boltzmann equation with long-range interactions ⋮ Kac's process with hard potentials and a moderate angular singularity ⋮ On the well-posedness of the spatially homogeneous Boltzmann equation with a moderate angular singularity ⋮ Hypocoercivity for perturbation theory and perturbation of hypocoercivity for confined Boltzmann-type collisional equations ⋮ High order approximation for the Boltzmann equation without angular cutoff under moderately soft potentials ⋮ Construction of Boltzmann and McKean-Vlasov type flows (the sewing lemma approach) ⋮ On the uniqueness for the spatially homogeneous Boltzmann equation with a strong angular singularity ⋮ Asymptotic analysis of the spatially homogeneous Boltzmann equation: grazing collisions limit ⋮ Well-posedness of spatially homogeneous Boltzmann equation with full-range interaction ⋮ A new approach to quantitative propagation of chaos for drift, diffusion and jump processes ⋮ Smoothing estimates for Boltzmann equation with full-range interactions: spatially inhomogeneous case ⋮ The Enskog process for hard and soft potentials ⋮ Finiteness of entropy for the homogeneous Boltzmann equation with measure initial condition ⋮ On the weak solution to the spatially homogeneous Boltzmann equation with moderate soft potentials

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations
• On Boltzmann equations and Fokker-Planck asymptotics: Influence of grazing collisions
• On the spatially homogeneous Boltzmann equation
• Invariant measures and evolution equations for Markov processes characterized via martingale problems
• Probabilistic interpretation and numerical approximation of a Kac equation without cutoff
• Probability metrics and uniqueness of the solution to the Boltzmann equation for a Maxwell gas
• A stochastic particle numerical method for 3D Boltzmann equations without cutoff
• An inequality for a functional of probability distributions and its application to Kac's one-dimensional model of a Maxwellian gas
• Probabilistic treatment of the Boltzmann equation of Maxwellian molecules