Global existence and decay properties for a degenerate Keller–Segel model with a power factor in drift term

The following degenerate parabolic system modelling chemotaxis is considered: where m 1, q 2, τ=0 or 1, and N 1. The aim of this paper is to prove the existence of a time global weak solution (u,v) of (KS) with the bound. Such a global bound is obtained in the case of (i) for large initial data and (ii) for small initial data. In the case of (ii), the decay properties of the solution (u,v) are also discussed.