Boundedness in a fully parabolic chemotaxis system with singular sensitivity

This paper deals with a fully parabolic chemotaxis system u(t) = Delta u - chi del (u/v del v), v(t) = Delta v - v + u with singular sensitivity x/v (chi > 0) on a bounded domain (Omega subset of R-n, n >= 2. The main result solves the open problem of tmiform-in-time boundedness of solutions for chi < root 2/n, which was conjectured by Winkler [16]. (C) 2014 Elsevier Inc. All rights reserved.