AMaSiS 2018 Workshop: Abstracts

Poster On a Poisson-Maxwell-Stefan model for isobaric isothermal electrically charged mixtures

Ansgar Jüngel and Oliver Leingang

TU Wien, Institute for Analysis and Scientific Computing

A new result addressing the global-in-time existence of weak solutions to a Poisson-Maxwell-Stefan system is presented. The model under consideration describes the dynamics of a charged multi-component mixture with N species in a bounded domain. The equations consist of a cross-diffusion system for the molar fractions, whereby the flux is only implicitly known through the Maxwell-Stefan equations, and a Poisson equation for the electric potential. After establishing the model, the key ideas of the existence proof and a new finite-element scheme, taking advantage of the entropy structure of this model, are presented. The main mathematical difficulties evolve from the lack of a maximum principle for this system, the treatment of different molar masses and the drift term involving the electrical potential.