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Séminaire du LJLL - 04 12 2020 14h00 : E. Zatorska
04 décembre 2020 — 14h00
à distance avec retransmission par Zoom
Ewelina Zatorska (Collège Impérial, Londres)
On the existence of solutions to the two-fluids systems
Résumé
In this talk I will present recent developments concerning the 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 models is the 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 systems, using a compactness criterion recently introduced by D. Bresch and P.-E. Jabin. I will also outline an innovative construction of solutions relying on the G. Crippa and C. De Lellis’ stability estimates for the transport equation. In the last part of my talk I will relate to a couple of more recent results : the existence of solutions to the one-dimensional system, and the non-uniqueness of solutions to the inviscid system. Finally I will comment on the issues around weak-strong uniqueness.