Thermodynamics and the Navier-Stokes equations: gas flow with phase transitions

We consider one-dimensional viscous gas flow described by the Navier-Stokes equations. Thermodynamic state of the gas obeys the van der Waals equation. This implies that phase transitions can occur along the flow of such gas. The corresponding solution is obtained as asymptotic expansion with respect to the parameters a and b from the van der Waals equation. The talk will also present a geometric approach to the thermodynamic states description.
Joint work with A.A. Gorinov, V.V. Lychagin, and S.N. Tychkov.