Boundedness in a chemotaxis system with weakly singular sensitivity in dimension two with arbitrary sub-quadratic degradation sources

We study the global existence and boundedness of solutions to a chemotaxis system with weakly singular sensitivity and sub-logistic sources in a two dimensional domain. X. Zhao (Nonlinearity; 2023; 36; 3909-3938) showed that the logistic degradation, - u², can prevent blow-up under the largeness assumption on. In this paper, we improve the result by replacing the quadratic degradation by sub-logistic one, - u²^ (u+e) with (0, 1), and removing the largeness assumption on.