Analysis and Mathematical Physics
Large Friction Limit of the Almost Pressureless Euler-Poisson System
The goal of this work is to investigate the almost pressureless Euler-Poisson (EP) system with repulsive force in the large friction limit. The leading order equations in the limit are shown to be the hyperbolic-elliptic Keller-Segel (KS) system of consumption type. Under suitable assumptions on the initial data, we establish the unique global-in-time solutions to both the EP system and the KS system by establishing the global stability in the large friction limit. In particular, no singularity forms in the asymptotic limit. Moreover, the time asymptotic behavior of the one-dimensional KS flow with vacuum is also discussed. In time permitted, I will also show some snapshots of the traveling wave solutions to a 1-d hyperbolic Keller-Segel system with quorum sensitivity.