Special Session 1: Analysis of parabolic models for chemotaxis

Global solvability and immediate regularization of measure-type population densities in a flux-limited Keller--Segel system

Shohei Kohatsu
Tokyo University of Science
Japan
Co-Author(s):    
Abstract:
We consider a flux-limited Keller--Segel system in a bounded domain, for which global existence and boundedness of classical solutions with linear diffusion and regular initial data were considered by Winkler (Math.\ Nachr.; 2022; 295; 1840--1862). It is shown that under conditions on the strength of diffusion and flux limitation, for any Radon measure initial data the system admits a global solution which immediately becomes smooth and classical, and approaches the given initial data in an appropriate sense.