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.
No takes yet. Share an insight, caveat, or question.
Ouyang et al. (2026) studied this question.
Synapse has enriched 5 closely related papers on similar clinical questions. Consider them for comparative context: