  We consider an attraction-repulsion chemotaxis model coupled with the
Navier-Stokes system. This model describes the interaction between a type of
cells (e.g., bacteria), which proliferate following a logistic law, and two
chemical signals produced by the cells themselves that degraded at a constant
rate. Also, it is considered that the chemoattractant is consumed with a rate
proportional to the amount of organisms. The cells and chemical substances are
transported by a viscous incompressible fluid under the influence of a force
due to the aggregation of cells. We prove the existence of global mild
solutions in bounded domains of RN , N = 2, 3, for small initial data in
Lp-spaces.
