Existence of Local Solutions for A Chemotaxis Navier Stokes System Modeling Cellular Swimming in Fluid Drops with Logistic Source (Al-Mukhtar Journal of Basic Sciences, 2026)
In this paper, we are concerned with the Cauchy problem for the three-dimensional chemotaxis system with an indirect signal production mechanism involving a diffusive partial differential equation. Which describes the motion of bacteria, Eukaryotes, in a fluid. Precisely, for the Chemotaxis-Navier–Stokes system modeling cellular swimming in fluid drops. We established the existence of local solutions to the compressible chemotaxis equation. We proved the local existence of the Cauchy problem (1.1)-(1.2) in  with the small initial data by using  the energy method.