Global solutions in a fully parabolic chemotaxis system with singular sensitivity

The Neumann boundary value problem for the chemotaxis system is considered in a smooth bounded domain Ω⊂ℝn, n⩾2, with initial data and v0∈W1, ∞(Ω) satisfying u0⩾0 and v0>0 in . It is shown that if then for any such data there exists a global-in-time classical solution, generalizing a previous result which asserts the same for n=2 only. Furthermore, it is seen that the range of admissible χ can be enlarged upon relaxing the solution concept. More precisely, global existence of weak solutions is established whenever . Copyright © 2010 John Wiley & Sons, Ltd.