Global weak solutions to a fully parabolic two-species chemotaxis system with fast p-Laplacian diffusion

We consider fully parabolic two-species chemotaxis system with (Formula presented.) -Laplacian diffusion in a smooth bounded domain (Formula presented.) with (Formula presented.) We show the existence of globally bounded weak solutions under the assumption that (Formula presented.) -norm of (Formula presented.) is bounded by a universal constant. We first get time-independent bounds for solution components of the approximate system. Then, pass the limit using Aubin–Lions lemma to get the solution candidate.