Blow-up for a three dimensional Keller-Segel model with consumption of chemoattractant

We investigate blow-up properties for the initial-boundary value problem of a Keller-Segel model with consumption of chemoattractant when the spatial dimension is three. Through a kinetic reformulation of the Keller-Segel system, we first derive some higher-order estimates and obtain certain blow-up criteria for the local classical solutions. These blow-up criteria generalize the results in [4,5] from the whole space R-3 to the case of bounded smooth domain Omega subset of R-3. Lower global blow-up estimate on parallel to n parallel to (infinity)(L)((Omega)) is also obtained based on our higher-order estimates. Moreover, we prove local non-degeneracy for blow-up points. (C) 2018 Elsevier Inc. All rights reserved.