In this lecture I will present broader spectrum of complex, multicomponent flows. For example, the models of compressible mixtures describe multicomponent fluids that are mixed on the molecular level. They are different from the models of the multi-phase flows from the first lecture, because there is no division of volume occupied by different species. The existence of global in time weak solutions, and global in time strong solutions for such systems will be explained, and some open problems related to singular limits and weak-strong uniqueness of solutions will be mentioned.
At the end of the lecture I will also present another model of two-phase flow describing the motion of compressible and incompressible medium with an interphase given by a condition on the density. I will explain how to prove the existence of solutions and give some applications in modelling of crowd evacuation.
Ewelina Zatorska obtained her PhD in 2013 from the University of Warsaw. She then held two postdoctoral positions: at Ecole Polytechnique Paris, and as the Chapman Fellowship of Imperial College London, along with Assistant Professorship at the University of Warsaw, and three visiting positions: Invited Professor at the Universite Paris Dauphine, Visiting Professor of the Waseda University in Tokyo, and the Fellow of the Institut Mittag-Leffler in Stockholm. In 2017 Ewelina became a Lecturer of the University College London, and in 2020 she moved to Imperial College London, where she works until today as a Senior Lecturer in the Applied and Numerical Analysis