Almost periodic solutions of the parabolic-elliptic Keller–Segel system on the whole space

In this paper, we investigate the existence and uniqueness of almost periodic solutions for the parabolic-elliptic Keller–Segel system on the whole space R n ( n ⩾ 4 ) . We work in the framework of critical spaces such as on the weak-Lorentz space L n 2 , ∞ ( R n ) . Our method is based on the dispersive and smoothing estimates of the heat semigroup and fixed point arguments.