Special Session 7: 

On the existence of solutions to the two-fluids systems

Ewelina Zatorska
University College London
Co-Author(s):    Didier Bresch, Piotr Mucha
The aim of this talk is to present the recent developments in the topic of existence of solutions to the two-fluid systems. I will discuss the application of approach developed by P.-L. Lions and E. Feireisl and explain the limitations of this technique in the context of multi-component flow models. A particular example of such a model is two-fluids Stokes system with single velocity field and two densities, and with an algebraic pressure law closure. I will present the existence result that uses the compactness criterion introduced for the Navier-Stokes system by D. Bresch and P.-E. Jabin. I will also mention an innovative construction of solutions relying on the G. Crippa and C. DeLellis stability estimates for the transport equation.