An entropy-level method for quantitative time-asymptotic in the Fokker-Planck model for fermions -- appearance of non saturation
Year: 2026
Type: preprint
Abstract: In this contribution we consider the Fokker-Planck equation for fermions, commonly known as the Fermi-Dirac-Fokker-Planck equation. This equation is a correction of the classical Fokker-Planck model that incorporates the Pauli exclusion principle. We present a novel approach that combines three ingredients: (1) stability of solutions, (2) quantitative convergence for a dense set of initial data via a robust entropy method, and (3) a De Giorgi level-set iteration, to establish quantitative time-asymptotic thermalisation for general initial data. In particular, we prove quantitative convergence for arbitrarily cold initial data.
Source: arXiv (Cornell University)
Authors: Alonso, R., Lods, B.
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7214699939