Global classical solution to a chemotaxis consumption model with singular sensitivity

In this paper, we are concerned with the chemotaxis consumption model with singular sensitivity {u(t) = Delta u - del.(f(u)/v del v), x is an element of Omega, t > 0, v(t) = Delta v - uv, x is an element of Omega, t > 0, under homogeneous Neumann boundary conditions in a smooth bounded domain Omega subset of R-n (n >= 1), for 0 < f (u) <= K (u + 1)(alpha) with some K > 0 and alpha < 2. It is shown that for any sufficiently smooth initial data, the above system admits a global classical solution when either n = 1 and alpha < 2, or n >= 2 and alpha < 1 - n/4. (C) 2017 Elsevier Ltd. All rights reserved.