Aggregated Steady States of a Kinetic Model for Chemotaxis

TL;DR

This paper analyzes a kinetic chemotaxis model with attractive interactions, demonstrating the existence of aggregated steady states under certain conditions, and revealing a critical mass phenomenon through a simplified moment system.

Contribution

It introduces a specific kinetic chemotaxis model with a novel turning operator that allows for closed moment systems and proves the existence of aggregated steady states for supercritical mass.

Findings

Existence of aggregated steady states for supercritical mass

Critical mass phenomenon in the second order moment system

Closed ODE systems for moments of arbitrary order

Abstract

A kinetic chemotaxis model with attractive interaction by quasistationary chemical signalling is considered. The special choice of the turning operator, with velocity jumps biased towards the chemical concentration gradient, permits closed ODE systems for moments of the distribution function of arbitrary order. The system for second order moments exhibits a critical mass phenomeneon. The main result is existence of an aggregated steady state for supercritical mass.