Some Recent Results about the Sixth Problem of Hilbert

  • Laure Saint-Raymond
Part of the Advances in Mathematical Fluid Mechanics book series (AMFM)


The sixth problem proposed by Hilbert, in the occasion of the International Congress of Mathematicians held in Paris in 1900, asks for a global understanding of the gas dynamics. For a perfect gas, the kinetic equation of Boltzmann provides a suitable model of evolution for the statistical distribution of particles. Hydrodynamic models are obtained as first approximations when collisions are frequent. In incompressible regime, rigorous convergence results are now established by describing precisely the corrections to the hydrodynamic approximation, namely physical phenomena such as relaxation or oscillations on small spatio-temporal scales, and checking that they do not disturb the mean motion.


Boltzmann Equation Local Thermodynamic Equilibrium Macroscopic Parameter Incompressible Euler Equation Microscopic Interaction 


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Copyright information

© Birkhäuser Verlag Basel/Switzerland 2006

Authors and Affiliations

  • Laure Saint-Raymond
    • 1
  1. 1.Laboratoire J.-L. Lions UMR 7598Université Paris VIParisFrance

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