Parabolic-elliptic Keller-Segel's system
Analysis of PDEs
2024-10-02 v1
Abstract
We study on the whole space R d the compressible Euler system with damping coupled to the Poisson equation when the damping coefficient tends towards infinity. We first prove a result of global existence for the Euler-Poisson system in the case where the damping is large enough, then, in a second step, we rigorously justify the passage to the limit to the parabolic-elliptic Keller-Segel after performing a diffusive rescaling, and get an explicit convergence rate. The overall study is carried out in 'critical' Besov spaces, in the spirit of the recent survey [16] by R. Danchin devoted to partially dissipative systems.
Cite
@article{arxiv.2307.05981,
title = {Parabolic-elliptic Keller-Segel's system},
author = {Valentin Lemarié},
journal= {arXiv preprint arXiv:2307.05981},
year = {2024}
}