Global Strong Solutions for Maxwell-Stefan Diffusion with Additive Friction Coefficients
Abstract
We study Maxwell-Stefan diffusion with additive friction coefficients fij=gi+gj. In mass fractions, the system isolates the constrained pair-friction block; in mole fractions, it is the classical ideal isothermal/isobaric Maxwell-Stefan system at constant total molar concentration. Additivity makes the constrained pair-friction dissipation species-diagonal; conversely, species-diagonality on one interior barycentric constraint space forces a pair-sum representation. At operator level, the positive constrained relaxation operator is a scalar shift of a compression of G=diag[g1,…,gN]. Its scalar resolvent yields both an explicit constrained inverse and interlacing spectral roots, which form global real-analytic coordinates on the open simplex and whose differentials are left eigen-covectors. In root coordinates the principal part is diagonal, no self-square gradient term occurs, and scalar comparison yields invariant rectangles and separation from the simplex boundary. For regularity we introduce entropy-stabilized one-sided multi-EPD truncations: Euler-Poisson-Darboux entropies cancel mixed quadratic production, while for N≥4 a truncation-weighted mixing-entropy correction supplies transverse coercivity. Caccioppoli and logarithmic estimates, shrinking, and critical mass yield Hölder continuity up to the Neumann boundary. The mixing entropy also symmetrizes the moment system; frozen conormal estimates give spatial Lipschitz bounds. Together with time Hölder control and short-interval maximal regularity, this yields global strong solvability on bounded C2+α domains with 0<α<1, for each N≥2, d≥2, and p>d+2, for all uniformly positive, compatible initial concentrations in the natural trace class. Solutions become classical for positive times and converge exponentially to equilibrium in relative entropy, L2, and C1(Ω̅).
Related
- Global Strong Solutions for the Ternary Maxwell-Stefan Diffusion System
- Global Strong Solutions for the Affine Darken Class of Maxwell-Stefan Diffusion Systems
- Strong solutions of SDEs with critical discontinuities in diffusion coefficients
- Optimization-based numerical methods for the two-and three-dimensional time harmonic Maxwell problem with sign-changing coefficients
- Finite Element Analysis of Maxwell's Equations with Time-Varying Coefficients and Nonlinear E-H Coupling: Convergence and Exponential Decay
BibTeX
@misc{bothe2026global,
title = {{Global Strong Solutions for Maxwell-Stefan Diffusion with Additive Friction Coefficients}},
author = {Dieter Bothe},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.06732},
eprint = {2609.06732},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.06732},
}
RIS
TY - UNPB
TI - Global Strong Solutions for Maxwell-Stefan Diffusion with Additive Friction Coefficients
AU - Dieter Bothe
PY - 2026
DA - 2026/09/06
PB - arXiv
DO - 10.48550/arxiv.2609.06732
UR - https://arxiv.org/abs/2609.06732
AB - We study Maxwell-Stefan diffusion with additive friction coefficients f_ij=g_i+g_j. In mass fractions, the system isolates the constrained pair-friction block; in mole fractions, it is the classical ideal isothermal/isobaric Maxwell-Stefan system at constant total molar concentration. Additivity makes the constrained pair-friction dissipation species-diagonal; conversely, species-diagonality on one interior barycentric constraint space forces a pair-sum representation. At operator level, the positive constrained relaxation operator is a scalar shift of a compression of G=diag[g_1,…,g_N]. Its scalar resolvent yields both an explicit constrained inverse and interlacing spectral roots, which form global real-analytic coordinates on the open simplex and whose differentials are left eigen-covectors. In root coordinates the principal part is diagonal, no self-square gradient term occurs, and scalar comparison yields invariant rectangles and separation from the simplex boundary. For regularity we introduce entropy-stabilized one-sided multi-EPD truncations: Euler-Poisson-Darboux entropies cancel mixed quadratic production, while for N≥4 a truncation-weighted mixing-entropy correction supplies transverse coercivity. Caccioppoli and logarithmic estimates, shrinking, and critical mass yield Hölder continuity up to the Neumann boundary. The mixing entropy also symmetrizes the moment system; frozen conormal estimates give spatial Lipschitz bounds. Together with time Hölder control and short-interval maximal regularity, this yields global strong solvability on bounded C^2+α domains with 0<α<1, for each N≥2, d≥2, and p>d+2, for all uniformly positive, compatible initial concentrations in the natural trace class. Solutions become classical for positive times and converge exponentially to equilibrium in relative entropy, L^2, and C^1(Ω̅).
ER -