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Erschienen in:
2007 | OriginalPaper | Buchkapitel
Some Recent Results about the Sixth Problem of Hilbert
verfasst von : Laure Saint-Raymond
Erschienen in: Analysis and Simulation of Fluid Dynamics
Verlag: Birkhäuser Basel
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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.