Hu, J., Jüngel, A., & Zamponi, N. (2024). Global weak solutions for a nonlocal multispecies Fokker–Planck–Landau system. Kinetic and Related Models. https://doi.org/10.3934/krm.2024007
The global-in-time existence of weak solutions to a spatially homogeneous multispecies Fokker–Planck–Landau system for plasmas in the three-dimensional whole space is shown. The Fokker–Planck–Landau system is a simplification of the Landau equations assuming a linearized, velocity-independent, and isotropic kernel. The resulting equations depend nonlocally and nonlinearly on the moments of the distribution functions via the multispecies local Maxwellians. The existence proof is based on a three-level approximation scheme, energy and entropy estimates, as well as compactness results, and it holds for both soft and hard potentials.
