Finite time blow up for critical wave equations in high dimensions

2004/04/03 by Borislav Yordanov, Borislav T. Yordanov, Qi S. Zhang +2 · 5 citations
Mathematics · Physics and Astronomy · #35L15 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Black Holes and Theoretical Physics #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Navier-Stokes equation solutions #math-ph #math.AP #math.MP #msc:35L15

paper · pdf · doi:10.48550/arxiv.math/0404055

arxiv created 2004/04/03 · openalex publication_date 2004/04/03 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that solutions to the critical wave equation below can not be global if the initial values are positive somewhere and nonnegative. This completes the solution to the famous blow up conjecture about critical semilinear wave equations of the form Δu - ∂²_t u + |u|^p = 0 in dimensions n ≥ 4. The lower dimensional case n ≤ 3 was settled many years earlier.

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