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## One dimensional hydrodynamic model of nuclear collisions

Recently a hydrodynamical description of low energy nuclear collisions between heavy ions is very popular. Nuclear matter is a symmetric homogeneous mixture of two kind of nuclear constituents: protons (positively charged) and neutrons (not charged). In Lagrangian form the Navier-Stokes system is given by: Let  the specific volume,  the velocity,  the internal energy,  the temperature,  the termal flux and  the stress then the compressible Navier-stokes system reads as follows:
for  and  where  is the conserved mass on a slab. Further, it is necessary to assume the so-called Clausius-Duhem inequality
where  is the specific entropy. The stress is given by
The first term is the effective pressure and the second is the phenomenological viscous stress (cf. Hasse, R.W. (1978) Approaches to nuclear friction, Reports on Progress in Physics 41, 1027 - 1101. ). The functions  and  are completely defined by
Here  and  are parameters of the so-called Skyrme interaction.  is the Boltzmann constant for our monoparticular gas and  is the Planck' s constant. The internal energy is given by
is a suitable chosen positive constant such that  for  and

A late reference: B. Ducomet Asymptotic behaviour for a non-monotone fluid in one dimension: the positive temperature case (2001) MMAS, 24, ???-???.

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collected and worked out by Wolfgang Sprößig, TU-Bergakademie Freiberg