The paper “Inertial manifolds via spatial averaging revisited“, co-authored by Anna Kostianko (Imperial College London), Xinhua Li (Lanzhou University), Chunyou Sun (Lanzhou University), and Sergey Zelik, has been published in the SIAM Journal of Mathematical Analysis. The paper gives a comprehensive study of inertial manifolds for semilinear parabolic equations and their smoothness using the spatial averaging method. The approach in the paper is universal in that it covers most of the known results obtained via this method as well as giving a number of new ones. A link to the published version on the SIAM page is here. A link to the final form arXiv version is here. The class of equations and one of the main theorems are shown in the image below.