New forms of non-relativistic and relativistic hydrodynamic equations as derived by the renormalization-group method - possible functional ansatz in the moment method consistent with Chapman-Enskog theory -

摘要

After a brief account of the derivation of the first-order relativistichydrodynamic equation as a construction of the invariant manifold ofrelativistic Boltzmann equation, we give a sketch of derivation of thesecond-order hydrodynamic equation (extended thermodynamics) both in thenonrelativistic and relativistic cases. We show that the resultant equationsuggests a novel ansatz for the functional form to be used in Grad momentmethod, which turns out to give the same expressions for the transportcoefficients as those given in the Chapman-Enskog theory as well as the novelexpressions for the relaxation times and lenghts allowing natural physicalinterpretaion.