Oberseminar Mathematik in den Naturwissenschaften: Ewelina Zatorska, On the Existence of Solutions to the Two-Fluids Systems
|Datum:||17.12.2020, 14:15 - 15:45 Uhr|
|Veranstalter:||Lehrstuhl für Mathematik VI (Mathematik in den Naturwissenschaften)|
|Vortragende*r:||Ewelina Zatorska, Department of Mathematics, Imperial College London|
via Zoom video conference (request the Zoom link from firstname.lastname@example.org).
In this talk I will present the recent developments in the topic of existence of solutions to the two-fluid systems. The compensated compactness technique of P.-L. Lions and E. Feireisl for single-component fluids has certain limitations, distinctly in the context of multi-component flow models. A particular example of such model is two-fluids Stokes system with single velocity field and two densities, and with an algebraic pressure law closure. The first result that I will present is the existence of weak solutions for such system, using compactness criterion introduced recently by D. Bresch and P.-E. Jabin. I will also outline an innovative construction of solutions relying on the G. Crippa and C. DeLellis stability estimates for the transport equation. In the last part of my talk I will relate to a couple of more recent results: existence of solutions to one-dimensional system, non-uniqueness of solutions to inviscid system, and I will comment on issues around weak-strong uniqueness.