A direct method for the regularity of the gain term in the Boltzmann equation

DOI10.1006/jmaa.1998.6141zbMath0913.76081OpenAlexW1977907152MaRDI QIDQ1276356

Xuguang Lu

Publication date: 27 January 1999

Published in: Journal of Mathematical Analysis and Applications (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1006/jmaa.1998.6141

zbMATH Keywords

general kernelsseparated variable kernels

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05)

Related Items (21)

Smoothing effects for classical solutions of the full Landau equation ⋮ A stochastic Galerkin method for the Boltzmann equation with uncertainty ⋮ Rate of convergence to equilibrium for the spatially homogeneous Boltzmann equation with hard potentials ⋮ Boundedness of the Stationary Solution to the Boltzmann Equation with Spatial Smearing, Diffusive Boundary Conditions, and Lions' Collision Kernel ⋮ Cooling process for inelastic Boltzmann equations for hard spheres. II: Self-similar solutions and tail behavior ⋮ On strong convergence to equilibrium for the Boltzmann equation with soft potentials ⋮ Smoothing effects for weak solutions of the spatially homogeneous Landau-Fermi-Dirac equation for hard potentials ⋮ On the convergence to equilibrium for the spatially homogeneous Boltzmann equation for Fermi-Dirac particles ⋮ Hypocoercivity for perturbation theory and perturbation of hypocoercivity for confined Boltzmann-type collisional equations ⋮ Sharp Regularizing Estimates for the Gain Term of the Boltzmann Collision Operator ⋮ PROPAGATION OF SINGULARITIES IN THE SOLUTIONS TO THE BOLTZMANN EQUATION NEAR EQUILIBRIUM ⋮ Exponential convergence to the Maxwell distribution for some class of Boltzmann equations ⋮ Gain of regularity for the relativistic collision operator ⋮ On the Boltzmann equation for Fermi-Dirac particles with very soft potentials: global existence of weak solutions ⋮ Global existence and full regularity of the Boltzmann equation without angular cutoff ⋮ Regularity theory for the spatially homogeneous Boltzmann equation with cut-off ⋮ Smoothing estimates for Boltzmann equation with full-range interactions: spatially homogeneous case ⋮ Hypocoercivity Based Sensitivity Analysis and Spectral Convergence of the Stochastic Galerkin Approximation to Collisional Kinetic Equations with Multiple Scales and Random Inputs ⋮ Equilibrium solution to the inelastic Boltzmann equation driven by a particle bath ⋮ The Boltzmann equation for Bose-Einstein particles: velocity concentration and convergence to equilibrium ⋮ On measure solutions of the Boltzmann equation. II: Rate of convergence to equilibrium

Cites Work

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• The Boltzmann equation and its applications
• A proof of the smoothing properties of the positive part of Boltzmann's kernel
• The mathematical theory of dilute gases
• Compactness in Boltzmann's equation via Fourier integral operators and applications. I, II
• Compactness in Boltzmann's equation via Fourier integral operators and applications. III
• Regularity in the boltzmann equation and the radon transform
• Regularity of the Gain Term and Strong $L^1 $ Convergence to Equilibrium for the Relativistic Boltzmann Equation
• Asymptotic Theory of the Boltzmann Equation

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