## Differential and Integral Equations

### On a model Boltzmann equation without angular cutoff

#### Abstract

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

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

Dates
First available in Project Euclid: 21 December 2012

https://projecteuclid.org/euclid.die/1356061239

Mathematical Reviews number (MathSciNet)
MR1750040

Zentralblatt MATH identifier
1013.76072

#### Citation

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.