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

Junichi Harada

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

Analysis of PDEs 2019-06-11 v1

Authors: Junichi Harada

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}.

Keywords

blow-up solutions type ii blowup energy critical heat equation five dimensional higher speed

Cite

@article{arxiv.1906.03976,
  title  = {A higher speed type II blowup for the five dimensional energy critical heat equation},
  author = {Junichi Harada},
  journal= {arXiv preprint arXiv:1906.03976},
  year   = {2019}
}

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