Global weak solutions to a fully parabolic two‐species chemotaxis system with fast pp‐Laplacian diffusion

We consider fully parabolic two‐species chemotaxis system with ‐Laplacian diffusion in a smooth bounded domain with We show the existence of globally bounded weak solutions under the assumption that ‐norm of 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.