Large friction limit of the almost pressureless Euler-Poisson system

TL;DR

This paper analyzes the large friction limit of the almost pressureless Euler-Poisson system with repulsive forces, showing convergence to the Keller-Segel system and establishing global solutions without singularities.

Contribution

It demonstrates the rigorous derivation of the Keller-Segel system as the large friction limit of the Euler-Poisson system and proves global stability and solutions.

Findings

Convergence of Euler-Poisson to Keller-Segel system in large friction limit

Existence of unique global-in-time solutions without singularities

Analysis of asymptotic behavior in one-dimensional flow with vacuum

Abstract

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.