A remarkable estimate for the solutions of the Boltzmann equation

DOI10.1016/0893-9659(92)90065-HzbMath0762.35090OpenAlexW1981660530MaRDI QIDQ1195685

Carlo Cercignani

Publication date: 5 January 1993

Published in: Applied Mathematics Letters (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/0893-9659(92)90065-h

zbMATH Keywords

collision kernelmoment of classical solutions

Mathematics Subject Classification ID

Integro-partial differential equations (45K05) PDEs in connection with fluid mechanics (35Q35) Transport processes in time-dependent statistical mechanics (82C70)

Related Items (13)

Weak solutions of the Boltzmann equation and energy conservation ⋮ Errata: Weak solutions of the Boltzmann equation and energy conservation ⋮ Conditions at infinity for boltzmann's equation. ⋮ Global weak solutions of the Boltzmann equation in a slab with diffusive boundary conditions ⋮ Galilean theory of dispersion for kinetic equations ⋮ Existence and trend to equilibrium of weak solutions of the boltzmann equation ⋮ Global weak solutions and uniform \(L^p\)-stability of the Boltzmann-Enskog equation ⋮ Strong solutions of the Boltzmann equation in one spatial dimension ⋮ \(L^1\) stability estimate for a one-dimensional Boltzmann equation with inelastic collisions. ⋮ Hydrodynamic limit of granular gases to pressureless Euler in dimension 1 ⋮ Virial estimates for hard spheres ⋮ Modeling Error in L¹for a Hierarchy of 1-D Discrete Velocity Models ⋮ Trend to equilibrium of weak solutions of the Boltzmann equation in a slab with diffusive boundary conditions.

Cites Work

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• On the Cauchy problem for Boltzmann equations: Global existence and weak stability
• Solution globale de l'équation de Boltzmann discrète pour les modèles spatiaux réguliers à 12 où à 20 vitesses (Global solution of the discrete Boltzmann equation for regular models with 12 or 20 velocities)
• Large-time behavior of discrete velocity Boltzmann equations
• Regularity of the moments of the solution of a transport equation
• Existence theorems for certain kinetic equations and large data
• The Boltzmann equation and its applications
• Global existence of solutions for a model Boltzmann equation
• On the Broadwell's model for a simple discrete velocity gas

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