Global solvability in a two-species chemotaxis system with signal production

TL;DR

This paper proves the global existence of solutions for a two-species chemotaxis system with competition and signal production, under weak damping conditions and integrable initial data, in bounded smooth domains.

Contribution

It establishes the first global existence results for this chemotaxis system with weak damping and minimal initial data assumptions.

Findings

Global solutions exist under sub-quadratic damping conditions.

Solutions are valid for initial data that are merely integrable.

The results apply to bounded smooth domains in any dimension.

Abstract

In this work, we study the Neumann initial-boundary value problem for a two-species chemotaxis system with Lotka-Volterra competition and signal production. Under a rather weak and clean condition of sub-quadratic type damping and merely integrable initial data, we establish the global existence of generalized solutions in an N dimensional bounded and smooth domain.