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Global Well-Posedness of Landau Equation in Bounded Domains
Abstract
We prove global well-posedness of the Landau equation near a Maxwellian in bounded C3 domains with in-flow or diffuse-reflection boundary conditions for −3≤γ≤1, including Coulomb interactions. Small compatible Gaussian perturbations generate global strong solutions, with uniqueness and continuous dependence among weak solutions. The proof combines energy estimates, the comparison principle, interior and weighted boundary estimates for velocity derivatives up to second order, and a logarithmic estimate for solution difference.
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BibTeX
@misc{ouyang2026global,
title = {{Global Well-Posedness of Landau Equation in Bounded Domains}},
author = {Zhimeng Ouyang and Lei Wu},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.40517},
eprint = {2610.40517},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.40517},
}
RIS
TY - UNPB
TI - Global Well-Posedness of Landau Equation in Bounded Domains
AU - Zhimeng Ouyang
AU - Lei Wu
PY - 2026
DA - 2026/10/29
PB - arXiv
DO - 10.48550/arxiv.2610.40517
UR - https://arxiv.org/abs/2610.40517
AB - We prove global well-posedness of the Landau equation near a Maxwellian in bounded C^3 domains with in-flow or diffuse-reflection boundary conditions for −3≤γ≤1, including Coulomb interactions. Small compatible Gaussian perturbations generate global strong solutions, with uniqueness and continuous dependence among weak solutions. The proof combines energy estimates, the comparison principle, interior and weighted boundary estimates for velocity derivatives up to second order, and a logarithmic estimate for solution difference.
ER -