Global Existence of Classical Solutions of Chemotaxis Systems with Logistic Source and Consumption or Linear Signal Production on Rn

While much literature on chemotaxis systems focuses on bounded domains, this paper emphasizes the global existence of classical solutions for three primary chemotaxis systems with a logistic source on Ian. We present a unified proof demonstrating global existence of solutions can be deduced from their locally uniform boundedness in Lp(Ian) for some p > max{1, n/2}. We then provide sufficient conditions for the global existence and boundedness of classical solutions. Notably, our findings even improve several existing results for bounded domains.