Differential and Integral Equations

On a model Boltzmann equation without angular cutoff

L. Desvillettes and F. Golse

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A model Boltzmann equation (see formulas (1.1.6) -- (1.1.9) below) without Grad's angular cutoff assumption is considered. One proves: 1) the instantaneous smoothing in both position and velocity variables by the evolution semigroup associated to the Cauchy problem for this model; 2) the derivation of the analogue of the Landau-Fokker-Planck equation in the limit when grazing collisions prevail.

Article information

Differential Integral Equations Volume 13, Number 4-6 (2000), 567-594.

First available in Project Euclid: 21 December 2012

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 76P05: Rarefied gas flows, Boltzmann equation [See also 82B40, 82C40, 82D05]
Secondary: 82C40: Kinetic theory of gases


Desvillettes, L.; Golse, F. On a model Boltzmann equation without angular cutoff. Differential Integral Equations 13 (2000), no. 4-6, 567--594. https://projecteuclid.org/euclid.die/1356061239.

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