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Congestion phenomena in fluid dynamics

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TURW02 - Rigorous analysis of incompressible fluid models and turbulence

This talk will be devoted to the mathematical analysis of fluid systems in which the total density cannot take values above a certain threshold. This type of system arises for instance in the description of crowd motion, or of diphasic flows with saturated regions. We will describe two ways of modeling the congestion: either the dynamics is compressible, with a pressure depending on the density and becoming singular when the density nears the threshold, or the dynamics couples compressible zones (where the density is far from the threshold) and incompressible zones (where the maximal density constraint is reached). We will focus on the question of the stability of travelling waves for two such models. This is a joint work with Charlotte Perrin.

This talk is part of the Isaac Newton Institute Seminar Series series.

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