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

Kleber Carrapatoso, Isabelle Gallagher and Isabelle Tristani
Vol. 8 (2026), No. 3, 497–538
DOI: 10.2140/tunis.2026.8.497
Abstract

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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Keywords
Boltzmann equation, Navier–Stokes–Fourier equation, hydrodynamical limit
Mathematical Subject Classification
Primary: 35Q20, 35Q30, 76D05, 76P05
Milestones
Received: 11 March 2025
Accepted: 24 September 2025
Published: 6 May 2026
Authors
Kleber Carrapatoso
Centre de Mathématiques Laurent Schwartz
École Polytechnique
Institut Polytechnique de Paris
Palaiseau
France
Isabelle Gallagher
Département de Mathématiques et applications
École normale supérieure
CNRS
Paris
France		 IMJ-PRJ
UFR de mathématiques
Université Paris Cité
Sorbonne Université
CNRS
Paris
France
Isabelle Tristani
Laboratoire J. A. Dieudonné
Université Côte d’Azur
CNRS
Nice
France
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