Global solutions in a fully parabolic chemotaxis system with singular sensitivity

The Neumann boundary value problem for the chemotaxis system {u(t) = Delta u-chi del.(u/v del v), x is an element of Omega, t>0, v(t) = Delta v-v+u, x is an element of Omega, t>0, is considered in a smooth bounded domain Omega subset of R(n), n >= 2, with initial data u(0)is an element of C(0)((Omega) over bar) and v(0)is an element of W(1,infinity)(Omega) satisfying u(0)>= 0 and v(0)>0 in (Omega) over bar. It is shown that if 0