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 L¹∩L^p, (n<p≤∞) for a chemotaxis system is given on the whole space Rn, 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.