# American Institute of Mathematical Sciences

August  2017, 10(4): 673-696. doi: 10.3934/dcdss.2017034

## Modeling and analysis of reactive multi-component two-phase flows with mass transfer and phase transition the isothermal incompressible case

 1 Technische Universität Darmstadt, D-64287 Darmstadt, Germany 2 Martin-Luther-Universität Halle-Wittenberg, Institut für Mathematik, Theodor-Lieser-Straße 5, D-06120 Halle, Germany

* Corresponding author: Jan Prüss

Received  June 2016 Revised  October 2016 Published  April 2017

Isothermal incompressible multi-component two-phase flows with mass transfer, chemical reactions, and phase transition are modeled based on first principles. It is shown that the resulting system is thermodynamically consistent in the sense that the available energy is a strict Lyapunov functional, and the equilibria are identified. It is proved that the problem is well-posed in an $L_p$-setting, and generates a local semiflow in the proper state manifold. It is further shown that each non-degenerate equilibrium is dynamically stable in the natural state manifold. Finally, it is proved that a solution, which does not develop singularities, exists globally and converges to an equilibrium in the state manifold.

Citation: Dieter Bothe, Jan Prüss. Modeling and analysis of reactive multi-component two-phase flows with mass transfer and phase transition the isothermal incompressible case. Discrete & Continuous Dynamical Systems - S, 2017, 10 (4) : 673-696. doi: 10.3934/dcdss.2017034
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A typical geometry
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