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:{A formula is presented} where m {greater than or slanted equal to} 1, q {greater than or slanted equal to} 2, τ = 0 or 1, and N {greater than or slanted equal to} 1. The aim of this paper is to prove the existence of a time global weak solution ( u, v) of (KS) with the L^∞ ( 0, ∞ ; L^∞ ( R^N ) ) bound. Such a global bound is obtained in the case of (i) m > q - frac(2, N) for large initial data and (ii) 1 {less-than or slanted equal to} m {less-than or slanted equal to} q - frac(2, N) for small initial data. In the case of (ii), the decay properties of the solution ( u, v ) are also discussed.