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

We consider the following chemotaxis system: (Formula presented.) 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.