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 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. [ABSTRACT FROM AUTHOR]