The Incompressible Navier-Stokes-Fourier Limits from Boltzmann-Fermi-Dirac Equation for Low Regularity Data
Analysis of PDEs
2025-09-26 v1
Abstract
We consider the hydrodynamic limits of the quantum Boltzmann equation with Fermi-Dirac statistics for hard sphere and hard potentials in the whole space. By analyzing the spectrum of the linearized collision operator combined with the transport operator and its associated semigroup, the incompressible Navier-Stokes-Fourier limits from the BFD equation is verified rigorously. Compared to the results in [Jiang-Xiong-Zhou,J. Differ. Equ.,2022], this paper works with a lower regularity for the initial data. In addition, the fixed-point arguments together with a time iteration ensure us to obtain the lifespan of kinetic solution coincides with those of limiting fluid solution.
Keywords
Cite
@article{arxiv.2509.21030,
title = {The Incompressible Navier-Stokes-Fourier Limits from Boltzmann-Fermi-Dirac Equation for Low Regularity Data},
author = {Ning Jiang and Chenchen Wang and Kai Zhou},
journal= {arXiv preprint arXiv:2509.21030},
year = {2025}
}
Comments
42 pages, no figures