Section: New Results

Lung and respiration modeling

Participants : Laurent Boudin, Bérénice Grec, Muriel Boulakia, Anne-Claire Egloffe, Céline Grandmont, Ayman Moussa.

• [9] : This paper is concerned with a system that couples the incompressible Navier–Stokes equations to the Vlasov–Fokker–Planck equation. Such a system arises in the modeling of sprays, where a dense phase interacts with a disperse phase. The coupling arises from the Stokes drag force exerted by a phase on the other.

• [25] : We are concerned with the global well-posedness of a two-phase flow system arising in the modelling of fluid-particle interactions. This system consists of the Vlasov-Fokker-Planck equation for the dispersed phase (particles) coupled to the incompressible Euler equations for a dense phase (fluid) through the friction forcing.

• [49] : We obtain the Maxwell-Stefan diffusion model by studying the asymptotic behaviour of a multicomponent kinetic model when the Knudsen number goes to 0.

• [50] : We are concerned here with identifiability, stability properties and estimates for the inverse problem of identifying a Robin coefficient on some non accessible part of the boundary from available data on the other part of boundary corresponding to solutions of the Stokes equations. We first study the identifiability of Robin coefficient and then we establish a stability estimate of logarithm type using Carleman inequality.