The Navier-Stokes limit of kinetic equations for low regularity data
Analysis of PDEs
2026-05-20 v1
Abstract
In this paper, we investigate the link between kinetic equations (including Boltzmann with or without cutoff assumption and Landau equations) and the incompressible Navier-Stokes equation. We work with strong solutions and we treat all the cases in a unified framework. The main purpose of this work is to be as accurate as possible in terms of functional spaces. More precisely, it is well-known that the Navier-Stokes equation can be solved in a lower regularity setting (in the space variable) than kinetic equations. Our main result allows to get a rigorous link between solutions to the Navier-Stokes equation with such low regularity data and kinetic equations.
Keywords
Cite
@article{arxiv.2503.12046,
title = {The Navier-Stokes limit of kinetic equations for low regularity data},
author = {Kleber Carrapatoso and Isabelle Gallagher and Isabelle Tristani},
journal= {arXiv preprint arXiv:2503.12046},
year = {2026}
}