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arXiv · 2503.12046

The Navier-Stokes limit of kinetic equations for low regularity data

Kleber Carrapatoso·Isabelle Gallagher·Isabelle Tristani
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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.

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Kleber Carrapatoso, Isabelle Gallagher, Isabelle Tristani. 2025-03-15. The Navier-Stokes limit of kinetic equations for low regularity data. https://doi.org/10.2140/tunis.2026.8.497

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