A higher speed type II blow-up for the 4-d Fujita equation

2022/09/18 by Jianfeng Zhao, Zhao, Jianfeng
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.2209.08580

openalex publication_date 2022/09/18 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

This paper is concerned with blow-up solutions of the 4-dimensional energy critical heat equation u_t=Δu + u³. Our main result is to show that the existence of type II blowup solutions, and ‖u(⋅,t)‖_∞∼(T-t)^-k|ln(T-t)|^(2k)/(2k-1), (k=1,2,3⋯).The inner-outer gluing method has been employed.

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