The Verigin problem with and without phase transition

  • Jan Prüss

    Martin-Luther-Universität Halle-Wittenberg, Germany
  • Gieri Simonett

    Vanderbilt University, Nashville, USA


Isothermal compressible two-phase flows with and without phase transition are modeled, employing Darcy’s and/or Forchheimer’s law for the velocity field. It is shown that the resulting systems are thermodynamically consistent in the sense that the available energy is a strict Lyapunov functional. In both cases, the equilibria are identified and their thermodynamical stability is investigated by means of a variational approach. It is shown that the problems are well-posed in an -setting and generate local semiflows in the proper state manifolds. It is further shown that a non-degenerate equilibrium is dynamically stable in the natural state manifold if and only if it is thermodynamically stable. Finally, it is shown that a solution which does not develop singularities exists globally and converges to an equilibrium in the state manifold.

Cite this article

Jan Prüss, Gieri Simonett, The Verigin problem with and without phase transition. Interfaces Free Bound. 20 (2018), no. 1, pp. 107–128

DOI 10.4171/IFB/398