Abstract
The classical Patlak-Keller-Segel system is a typical model that, byreaction-diffusion equations, describes the chemotaxis process. In another hand, the cellscommonly are in an incompressible viscous fluid, then the cells and chemical substrates arealso transported by the fluid. The motion of the fluid is determined by the incompressibleNavier-Stokes equations or Stokes equations, so it i…