The Chemotaxis-Navier Stokes Equations in Bounded Domain

When bacteria of the species Bacillus subtilis are suspended in water it can be observed experimentally that spatial patterns may spontaneously emerge from initially almost homogeneous distributions of bacteria. A mathematical model for such processes was proposed in many literatures where it is assumed that the essentially responsible mechanisms are a chemotactic movement of bacteria towards oxygen which they consume a gravitational effect on the motion of the fluid by the heavier bacteria and a convective transport of both cells and oxygen through the water. We've studied chemotaxis-Navier-Stokes systems for several years and obtained some important results. In the current edition we synthesis and analysis these results as well as make our effort to give the proofs of them in detail and perfectly. However in this process we have benefited enormously. In conclusion we hope that the interested scientist will enjoy this book and derive great benefit from reading it just as we did while writing it.