A variational principle for two-fluid models
  A variational principle for two-fluid mixtures is proposed. The Lagrangian is constructed as the difference between the kinetic energy of the mixture and a thermodynamic potential conjugated to the internal energy with respect to the relative velocity of phases. The equations of motion and a set of Rankine-Hugoniot conditions are obtained. It is proved also that the convexity of the internal energy guarantees the hyperbolicity of the one-dimensional equations of motion linearized at rest. 
Sergey Gavrilyuk, Henri Gouin (MSNMGP, LMMT), Yurii Perepechko