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Caltech/UCLA/USC Joint Analysis Seminar

Tuesday, October 25, 2022
12:30pm to 1:30pm
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The dissipative Aw-Rascle system: existence theory and hard-congestion limit
Ewelina Zatorska, Department of Mathematics, Imperial College London,

In this talk I am going to analyze the compressible dissipative hydrodynamic model of crowd motion or of granular flow. The model resembles the famous Aw-Rascle model of traffic, except that the difference between the actual and the desired velocities (the offset function) is a gradient of the density function, and not a scalar. This modification gives rise to a dissipation term in the momentum equation that vanishes when the density is equal to zero.
I will compare the dissipative Aw-Rascle system with the compressible Euler and compressible Navier-Stokes equations, and back it up with two existence and ill-posedness results. In the last part of my talk I will explain the proof of conjecture made by Lefebvre-Lepot and Maury, that the hard congestion limit of this system (with singular offset function) leads to congested compressible/incompressible Euler equations.

For more information, please contact Math Department by phone at 626-395-4335 or by email at [email protected] or visit