The Incompressible Navier-stokes Limit of the Boltzmann Equation for Hard Cutoff Potentials

@inproceedings{Golse2009TheIN,
  title={The Incompressible Navier-stokes Limit of the Boltzmann Equation for Hard Cutoff Potentials},
  author={François Golse and Laure Saint-Raymond},
  year={2009}
}
The present paper proves that all limit points of sequences of renormalized solutions of the Boltzmann equation in the limit of small, asymptotically equivalent Mach and Knudsen numbers are governed by Leray solutions of the Navier-Stokes equations. This convergence result holds for hard cutoff potentials in the sense of H. Grad, and therefore completes earlier results by the same authors [Invent. Math. 155, 81-161 (2004)] for Maxwell molecules. 
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From Boltzmann equation to Navier-Stokes equations I

  • P.-L. Lions, N. Masmoudi
  • Arch. Ration. Mech. Anal. 158
  • 2001
Highly Influential
9 Excerpts

On the Cauchy Problem for the Boltzmann Equation: Global Existence and Weak Stability Results

  • R. J. DiPerna, P.-L. Lions
  • Annals of Math. 130
  • 1989
Highly Influential
18 Excerpts

The Navier-Stokes limit of the Boltzmann equation for bounded collision kernels

  • F. Golse, L. Saint-Raymond
  • Invent. Math. 155
  • 2004
Highly Influential
9 Excerpts

Fluid Dynamic Limits of the Boltzmann Equation II: Convergence Proofs

  • C. Bardos, F. Golse, C. D. Levermore
  • Comm. Pure Appl. Math. 46
  • 1993
Highly Influential
6 Excerpts

From particles to fluids

  • R. Esposito, M. Pulvirenti
  • Handbook of mathematical fluid dynamics. 3, 1–82…
  • 2004
1 Excerpt

From the BGK model to the Navier-Stokes equations

  • L. Saint-Raymond
  • Ann. Sci. École Norm. Sup. 36
  • 2003
2 Excerpts

Discrete time Navier-Stokes limit for the BGK Boltzmann equation

  • L. Saint-Raymond
  • Comm. Partial Diff. Eq. 27
  • 2002
2 Excerpts

The Stokes-Fourier and Acoustic Limits for the Boltzmann Equation

  • F. Golse, C. D. Levermore
  • Comm. on Pure and Appl. Math. 55
  • 2002
1 Excerpt

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