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arXiv · 2610.40517

Global Well-Posedness of Landau Equation in Bounded Domains

Zhimeng Ouyang·Lei Wu
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Abstract

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 $-3\leqγ\leq1$, 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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Zhimeng Ouyang, Lei Wu. 2026-10-29. Global Well-Posedness of Landau Equation in Bounded Domains. https://arxiv.org/abs/2610.40517

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