Entropy Principle and Galilean Relativity for Dense Gases, the General Solution without Approximations

The many moments model for dense gases and macromolecular fluids is here considered, where the upper order moment is chosen in according to the suggestions of the non relativistic limit of the corresponding relativistic model. Solutions of the restrictions imposed by the entropy principle and that of Galilean relativity were until now obtained in literature by using Taylor expansions around equilibrium and without proving convergence. Here an exact solution without using expansions is found. The particular case with only 14 moments has already been treated in literature with a completely different way. Here it is proved that this particular closure is included in the present more general one.