From the Boltzmann equation to an incompressible Navier-Stokes-Fourier system

C. David Levermore, Nader Masmoudi

Research output: Contribution to journalArticlepeer-review


We establish a Navier-Stokes-Fourier limit for solutions of the Boltzmann equation considered over any periodic spatial domain of dimension two or more. We do this for a broad class of collision kernels that relaxes the Grad small deflection cutoff condition for hard potentials and includes for the first time the case of soft potentials. Appropriately scaled families of DiPerna-Lions renormalized solutions are shown to have fluctuations that are compact. Every limit point is governed by a weak solution of a Navier-Stokes-Fourier system for all time.

Original languageEnglish (US)
Pages (from-to)753-809
Number of pages57
JournalArchive for Rational Mechanics and Analysis
Issue number3
StatePublished - Jun 2010

ASJC Scopus subject areas

  • Analysis
  • Mathematics (miscellaneous)
  • Mechanical Engineering


Dive into the research topics of 'From the Boltzmann equation to an incompressible Navier-Stokes-Fourier system'. Together they form a unique fingerprint.

Cite this