The theory of the nonlinear Boltzmann equation for Maxwell molecules in Fourier representation

DOI10.1007/BF01759387zbMath0874.45005MaRDI QIDQ678138

Giuseppe Toscani, Ada Pulvirenti

Publication date: 2 November 1997

Published in: Annali di Matematica Pura ed Applicata. Serie Quarta (Search for Journal in Brave)

zbMATH Keywords

Cauchy problemnonlinear Boltzmann equationFourier representationMaxwell molecules

Mathematics Subject Classification ID

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

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Cites Work

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• Intermolecular forces of infinite range and the Boltzmann equation
• On the Cauchy problem for Boltzmann equations: Global existence and weak stability
• \(L^ p\)-estimates for the nonlinear spatially homogeneous Boltzmann equation
• Stability in \(L^ 1\) for the spatially homogeneous Boltzmann equation
• Global \(L^ p\)-properties for the spatially homogeneous Boltzmann equation
• Convergence towards equilibrium for a gas of Maxwellian pseudomolecules
• The Boltzmann equation and its applications
• Bivariate distributions with given marginals
• An inequality for certain functional of multidimensional probability distributions
• About the regularizing properties of the non-cut-off Kac equation
• THE FOKKER-PLANCK ASYMPTOTICS OF THE BOLTZMANN COLLISION OPERATOR IN THE COULOMB CASE
• On the generalization of the Boltzmann H-theorem for a spatially homogeneous Maxwell gas
• 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
• Stability and exponential convergence in Lp for the spatially homogeneous Boltzmann equation