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arXiv · 2305.17447

Global weak solutions for a nonlocal multispecies Fokker-Planck-Landau system

Jingwei Hu·Ansgar Jüngel·Nicola Zamponi
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Abstract

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.

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Jingwei Hu, Ansgar Jüngel, Nicola Zamponi. 2023-05-27. Global weak solutions for a nonlocal multispecies Fokker-Planck-Landau system. https://arxiv.org/abs/2305.17447

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