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 Double-struck capital Rd(d >= 2)$$ {\mathrm{\mathbb{R}}}<^>d\kern0.1em \left(d\ge 2\right) $$, which can describe the memory effect and anomalous diffusion of the considered system. The local and global existence and uniqueness in weak Lp$$ {L}<^>p $$ space are obtained by means of abstract fixed point theorem. Moreover, we explore the asymptotic stability of solutions as time goes to infinity.