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 $u_t=\mathrm{\Delta }u+|u{|}^{\frac{4}{3}}u$. A goal of this paper is to show the existence of type II blowup solutions which behave as $\Vert u(t){\Vert }_{\infty }\sim (T-t{)}^{-3k}$ ($k=2,3,\cdots$). These solutions are the same ones formally derived by Filippas, Herrero and Velázquez [8]. We find a mistake in their blowup rate and correct it.