Degond, P.; Lucquin-Desreux, B. The Fokker-Planck asymptotics of the Boltzmann collision operator in the Coulomb case. (English) Zbl 0755.35091 Math. Models Methods Appl. Sci. 2, No. 2, 167-182 (1992). Our main concern is the Boltzmann operator for Coulomb collisions and its Fokker-Planck approximation. In the case of Coulomb collisions, the scattering cross-section has a non-integrable singularity when the relative velocity of the colliding particles tends to zero and a careful analysis is required. Furthermore, by a scaling of the collision operator, the small parameter which is involved in the Fokker-Planck asymptotics is clearly identified to the plasma parameter, and an expansion which is consistent with the physical observations is derived. Cited in 2 ReviewsCited in 73 Documents MSC: 35Q35 PDEs in connection with fluid mechanics 82C31 Stochastic methods (Fokker-Planck, Langevin, etc.) applied to problems in time-dependent statistical mechanics 76X05 Ionized gas flow in electromagnetic fields; plasmic flow 76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics Keywords:Boltzmann equation; Boltzmann operator for Coulomb collisions PDFBibTeX XMLCite \textit{P. Degond} and \textit{B. Lucquin-Desreux}, Math. Models Methods Appl. Sci. 2, No. 2, 167--182 (1992; Zbl 0755.35091) Full Text: DOI