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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.

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
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