Global classical solutions to a chemotaxis consumption system with nonlinear sensitivity and signal consumption

Abstract

We consider the following chemotaxis system: ut =Δu−∇·(u∇f(v)), x∈ Ω, t>0, vt =Δv−ug(v), x∈ Ω, t>0, under homogeneous Neumann boundary conditions in a bounded smooth domain Ω ⊂ Rn,n=2,3 with nonlinear functions f and g. We establish the existence of a global classical solution under the smallness assumption on initial data. This result generalizes the existing findings for the minimal case, where f(s)=s and g(s)=s. We further present blow-up criteria for the system.