Existence and asymptotic stability of mild solution to fractional Keller‐Segel‐Navier‐Stokes system

This paper investigates the Cauchy problem for time‐space fractional Keller‐Segel‐Navier‐Stokes model in , which can describe the memory effect and anomalous diffusion of the considered system. The local and global existence and uniqueness in weak space are obtained by means of abstract fixed point theorem. Moreover, we explore the asymptotic stability of solutions as time goes to infinity.