Abstract
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 language | English (US) |
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Pages (from-to) | 753-809 |
Number of pages | 57 |
Journal | Archive for Rational Mechanics and Analysis |
Volume | 196 |
Issue number | 3 |
DOIs | |
State | Published - Jun 2010 |
ASJC Scopus subject areas
- Analysis
- Mathematics (miscellaneous)
- Mechanical Engineering