On strong convergence to equilibrium for the Boltzmann equation with soft potentials

DOI10.1007/s10955-009-9741-1zbMath1191.76087arXiv0808.1064OpenAlexW1978494436MaRDI QIDQ2390964

Xuguang Lu, Eric Anders Carlen, Maria Conception Carvalho

Publication date: 10 August 2009

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

Full work available at URL: https://arxiv.org/abs/0808.1064

zbMATH Keywords

convergence rateentropy inequalitiesmoment estimatesintegrable angular cutoff

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) Kinetic theory of gases in time-dependent statistical mechanics (82C40)

Related Items (15)

Rates of convergence to equilibrium for collisionless kinetic equations in slab geometry ⋮ On the homogeneous Boltzmann equation with soft-potential collision kernels ⋮ On the convergence to equilibrium for the spatially homogeneous Boltzmann equation for Fermi-Dirac particles ⋮ De Giorgi argument for weighted \(L^2\cap L^{\infty}\) solutions to the non-cutoff Boltzmann equation ⋮ Asymptotic analysis of the linearized Boltzmann collision operator from angular cutoff to non-cutoff ⋮ On backward solutions of the spatially homogeneous Boltzmann equation for Maxwelian molecules ⋮ Emergence of exponentially weighted L^p-norms and Sobolev regularity for the Boltzmann equation ⋮ On measure solutions of the Boltzmann equation. I: Moment production and stability estimates ⋮ On the rate of convergence to equilibrium for the linear Boltzmann equation with soft potentials ⋮ The spatially homogeneous Boltzmann equation for Bose-Einstein particles: rate of strong convergence to equilibrium ⋮ Propagation of uniform upper bounds for the spatially homogeneous relativistic Boltzmann equation ⋮ On semi-classical limit of spatially homogeneous quantum Boltzmann equation: weak convergence ⋮ Lower bound for the Boltzmann equation whose regularity grows tempered with time ⋮ On measure solutions of the Boltzmann equation. II: Rate of convergence to equilibrium ⋮ On the weak solution to the spatially homogeneous Boltzmann equation with moderate soft potentials

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Intermolecular forces of infinite range and the Boltzmann equation
• Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials
• Regularity estimates via the entropy dissipation for the spatially homogeneous Boltzmann equation without cut-off
• The Boltzmann equation with a soft potential. I: Linear, spatially- homogeneous
• The Boltzmann equation with a soft potential. II: Nonlinear, spatially- periodic
• The Boltzmann equation and its applications
• A proof of the smoothing properties of the positive part of Boltzmann's kernel
• On a new class of weak solutions to the spatially homogeneous Boltzmann and Landau equations
• A direct method for the regularity of the gain term in the Boltzmann equation
• Propagation of smoothness and the rate of exponential convergence to equilibrium for a spatially homogeneous Maxwellian gas
• On Boltzmann equations and Fokker-Planck asymptotics: Influence of grazing collisions
• Entropy dissipation and moment production for the Boltzmann equation
• Some applications of the method of moments for the homogeneous Boltzmann and Kac equations
• The mathematical theory of dilute gases
• Compactness in Boltzmann's equation via Fourier integral operators and applications. I, II
• Fast and slow convergence to equilibrium for Maxwellian molecules via wild sums
• Entropy dissipation and long-range interactions
• On the trend to equilibrium for some dissipative systems with slowly increasing a priori bounds.
• Sharp entropy dissipation bounds and explicit rate of trend to equilibrium for the spatially homogeneous Boltzmann equation
• Cercignani's conjecture is sometimes true and always almost true
• Entropy production estimates for Boltzmann equations with physically realistic collision kernels
• Conservation of energy, entropy identity, and local stability for the spatially homogeneous Boltzmann equation
• Exponential decay for soft potentials near Maxwellian
• Global solutions of Boltzmann's equation and the entropy inequality
• Régularité et compacité pour des noyaux de collision de Boltzmann sans troncature angulaire
• Regularity in the boltzmann equation and the radon transform

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