This paper concerns the uniform boundedness and global existence of solutions in time for the chemotaxis model with two chemicals. We prove the system has global existence of solutions in time for any dimension .
Qian Xu. Xiaolin Liu. Li Zhang. "The Global Existence of Solutions in Time for a Chemotaxis Model with Two Chemicals." J. Appl. Math. 2014 1 - 7, 2014. https://doi.org/10.1155/2014/186125