On the Cauchy problem for the discrete Boltzmann equation with initial values in \(L^ +_ 1{\mathbb{R}}\)

DOI10.1007/BF01218627zbMath0719.35073MaRDI QIDQ2640059

Giuseppe Toscani

Publication date: 1989

Published in: Communications in Mathematical Physics (Search for Journal in Brave)

zbMATH Keywords

Cauchy problemBoltzmann equationglobally solvableweighted \(L^ p\)- space

Mathematics Subject Classification ID

PDEs in connection with fluid mechanics (35Q35) Rarefied gas flows, Boltzmann equation in fluid mechanics (76P05) First-order nonlinear hyperbolic equations (35L60)

Related Items (6)

Global solutions to the initial-boundary value problem for the discrete Boltzmann equation ⋮ Large time behavior of the Broadwell model of a discrete velocity gas with specularly reflective boundary conditions ⋮ Existence globale à données d'entropie localement finie pour les modèles discrets de l'équation de Boltzmann avec termes linéaires et quadratiques ⋮ Existence and stability of stationary solutions to the discrete Boltzmann equation ⋮ A new contribution to nonlinear stability of a discrete velocity model ⋮ Large deviations from a kinetic limit

Cites Work

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• Large-time behavior of the Broadwell model of a discrete velocity gas
• The Broadwell model for initial values in \(L_+^ 1({\mathbb{R}})\)
• Large-time behavior of discrete velocity Boltzmann equations
• Discrete velocity models with small data
• The Boltzmann equation. I. Uniqueness and local existence
• Global existence and asymptotic behavior for the discrete velocity models of the Boltzmann equation
• On the Broadwell's model for a simple discrete velocity gas

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