Global existence of classical solutions of chemotaxis systems with logistic source and consumption or linear signal production on ${\mathbb{R}}^n$

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 ${\mathbb{R}}^n$. We present a unified proof demonstrating global existence of solutions can be deduced from their locally uniform boundedness in $L^p({\mathbb{R}}^n)$ for some $p>\max \{1,\frac{n}{2}\}$. 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.