Global solutions to a chemotaxis system with non-diffusive memory

In this article, an existence theorem of global solutions with small initial data belonging to L 1 ∩ L p , ( n < p ⩽ ∞ ) for a chemotaxis system is given on the whole space R n , n ⩾ 3 . In the case p = ∞ , our global solution is integrable with respect to the space variable on some time interval, and then conserves the mass for a short time, at least. The system consists of a chemotaxis equation with a logarithmic term and an ordinary equation without diffusion term.