  The objective is to investigate the global existence of solutions for a
degenerate chemotaxis system with logistic sources in a two-dimensional domain.
It is demonstrated that the inclusion of logistic sources can exclude the
occurrence of blow-up solutions, even in the presence of superlinear growth in
the cross-diffusion rate. Our proof relies on the application of elliptic and
parabolic regularity in Orlicz spaces and variational approach.
