LAUSR

Abstract Global existence is established for classical solutions to a chemotaxis model with signal-dependent motility for a general class of motility functions γ which may in particular decay in an arbitrary way at infinity. Assuming further that γ is non-increasing and decays sufficiently slowly at infinity, in the sense that γ ( s ) ∼ s − k as s → ∞ for some k ∈ ( 0 , N / ( N − 2 ) + ) , it is also shown that global solutions are uniformly bounded with respect to time. The admissible decay of γ at infinity here is higher than in previous works.