Global existence for the kinetic chemotaxis model without pointwise memory effects, and including internal variables

TL;DR

This paper proves global existence for a kinetic chemotaxis model incorporating internal variables and complex molecular networks, using dispersion and Strichartz estimates under specific growth conditions on the turning kernel.

Contribution

It extends previous models by including internal variables and provides a rigorous proof of global existence without pointwise memory effects.

Findings

Global existence established for the kinetic chemotaxis model

Inclusion of internal variables models complex molecular networks inside cells

Uses dispersion and Strichartz estimates under borderline growth assumptions

Abstract

This paper is concerned with the kinetic model of Othmer-Dunbar-Alt for bacterial motion. Following a previous work, we apply the dispersion and Strichartz estimates to prove global existence under several borderline growth assumptions on the turning kernel. In particular we study the kinetic model with internal variables taking into account the complex molecular network inside the cell.