The Fokker-Planck asymptotics of the Boltzmann collision operator in the Coulomb case. (English) Zbl 0755.35091

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.


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
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