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

Hu, Jingwei; Jüngel, Ansgar; Zamponi, Nicola

doi:10.3934/krm.2024007

Title: Global weak solutions for a nonlocal multispecies Fokker–Planck–Landau system

Journal Article · 05 December 2024 · Kinetic and Related Models

DOI: https://doi.org/10.3934/krm.2024007 · OSTI ID:2338060

Hu, Jingwei ^[1]; Jüngel, Ansgar ^[2]; Zamponi, Nicola ^[3]

University of Washington, Seattle, WA (United States); Michigan State University
Technische Universit¨at Wien (Austria)
Universität Ulm (Germany)

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. Furthermore, 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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Research Organization:: University of Washington, Seattle, WA (United States)

Sponsoring Organization:: USDOE Office of Science (SC); National Science Foundation (NSF); Air Force Office of Scientific Research (AFOSR); European Research Council (ERC)

Grant/Contract Number:: SC0023164

OSTI ID:: 2338060

Journal Information:: Kinetic and Related Models, Journal Name: Kinetic and Related Models Journal Issue: 6 Vol. 17; ISSN 1937-5093

Publisher:: American Institute of Mathematical SciencesCopyright Statement

Country of Publication:: United States

Language:: English

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