Global Strong Solutions for the Ternary Maxwell-Stefan Diffusion System
Abstract
We prove global strong well-posedness for the normalized isothermal, isobaric ternary Maxwell-Stefan diffusion system on bounded C2+α0 domains, for arbitrary positive constant binary frictions and compatible nonnegative initial data, without a smallness condition. For distinct frictions, trace--determinant variables produce two separated spectral roots satisfying scalar parabolic equations with antisymmetric quadratic coupling. Euler-Poisson-Darboux one-sided truncations, stabilized by the mixing entropy, yield boundary De Giorgi oscillation decay and positive-time Hölder regularity. The mixing-entropy Hessian then provides a local symmetrizer; conormal Schauder estimates give uniform C1+a control, and frozen maximal Lp-regularity yields a uniform terminal trace bound excluding finite-time breakdown. Repeated frictions reduce to triangular scalar parabolic systems. Every component with positive conserved mass is strictly positive for positive time.
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BibTeX
@misc{bothe2026global,
title = {{Global Strong Solutions for the Ternary Maxwell-Stefan Diffusion System}},
author = {Dieter Bothe},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.00162},
eprint = {2610.00162},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.00162},
}
RIS
TY - UNPB
TI - Global Strong Solutions for the Ternary Maxwell-Stefan Diffusion System
AU - Dieter Bothe
PY - 2026
DA - 2026/10/01
PB - arXiv
DO - 10.48550/arxiv.2610.00162
UR - https://arxiv.org/abs/2610.00162
AB - We prove global strong well-posedness for the normalized isothermal, isobaric ternary Maxwell-Stefan diffusion system on bounded C^2+α_0 domains, for arbitrary positive constant binary frictions and compatible nonnegative initial data, without a smallness condition. For distinct frictions, trace--determinant variables produce two separated spectral roots satisfying scalar parabolic equations with antisymmetric quadratic coupling. Euler-Poisson-Darboux one-sided truncations, stabilized by the mixing entropy, yield boundary De Giorgi oscillation decay and positive-time Hölder regularity. The mixing-entropy Hessian then provides a local symmetrizer; conormal Schauder estimates give uniform C^1+a control, and frozen maximal L_p-regularity yields a uniform terminal trace bound excluding finite-time breakdown. Repeated frictions reduce to triangular scalar parabolic systems. Every component with positive conserved mass is strictly positive for positive time.
ER -