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The hydrodynamical limit

The Boltzmann equation, when the gas is out of equilibrium, is an hard mathematical problem which is unresolved apart from very exceptional situations. The kinetic theory of non-uniform elastic gases near equilibrium, mainly due to Sydney Chapman and David Enskog [62], has been successful in establishing a method to derive the transport coefficients from the Boltzmann equation, obtaining closed hydrodynamic equations. It is interesting to mention that the first non-equilibrium solutions of the Boltzmann equation were presented by Enskog in his Ph.D thesis [80], defended in 1917 at the University of Uppsala, Sweden. In the late 40s H. Grad [99] developed an alternative mathematically equivalent method to obtain the same results. In this section we review the main passages of the kinetic theory of non-equilibrium elastic gases in order to have a reference frame for the next section, where the granular kinetics will be presented.



Subsections

Andrea Puglisi 2001-11-14