Attractors of non-autonomous reaction–diffusion equations in LpLp

In this paper, a new theorem which is proved in [S.S. Lu, H.Q. Wu, C.K. Zhong, Attractors for non-autonomous 2D Navier–Stokes equations with normal external forces, Discrete Contin. Dyn. Syst. 13 (3) (2005) 701–719] is applied to a nonlinear reaction–diffusion equation with normal forces. We obtain the existence of the uniform attractor in LpLp without any restriction on the growing order of the nonlinear term. The attractor attracts all bounded subsets of LpLp in the norm of LpLp.