A higher speed type II blowup for the five dimensional energy critical heat equation

Abstract: This paper is concerned with blow-up solutions of the five dimensional energy critical heat equation $u_t=\Delta u+|u|^\frac{4}{3}u$. A goal of this paper is to show the existence of type II blowup solutions which behave as $|u(t)|_\infty\sim(T-t)^{-3k}$ ($k=2,3,\cdots$). Our solutions are the same one formally derived by Filippas, Herrero and Vel\'azquez \cite{Filippas}.