| Abstract: |
| I plan to talk about the issue of existence of weak solutions to a simple model of a bi-fluid. In rough words, we consider a fluid characterized by two densities of ingredients, and the mathematical model is set by two continuity equations and the Stokes law defining a potential velocity in terms of pressure described by two densities of the fluid.
Adapting a brand new tool of compactness developed by D Bresch and PE Jabin we are able to construct solutions, using a novel approach based on the Lagrangian coordinates. What is important to underline, there is no parabolic regularization of continuity equations, and the form of the pressure does not allow to use the standard Lions-Feireisl approach.
The talk based on resutls joint with Didier Bresch and Ewelina Zatorska. |
|