Talk
On thick spray equations
Talk by Dr. Lucas Ertzbischoff
Date: 19.10.23 Time: 16.15 - 18.00 Room: ETH HG G 19.2
We consider a coupled system between kinetic and fluid equations, describing a cloud of particles immersed within a gas. In the "thick spray" regime, the volume fraction for the particles is not negligible compared to that of the fluid: it raises many difficulties for the study of such system, which seems to present losses of derivatives. In particular, and contrary to some other fluid-kinetic couplings, its mathematical study has almost remained absent. I will review some recent progress on thick spray equations, and show that one can actually build a Cauchy theory in Sobolev regularity (at least for a compressible viscous fluid) when the initial data satisfies a Penrose type stability condition (being in fact necessary and sufficient for well-posedness). This is based on joint works with Aymeric Baradat (CNRS, Université Lyon 1) and Daniel Han-Kwan (CNRS, Nantes Université).''