Norm inflation for the viscous nonlinear wave equation

2023/08/15 by Pierre Roubin, Mamoru Okamoto, de Roubin, Pierre +1
Mathematics · #35B30 #35L05 #35Q35 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Spectral Theory in Mathematical Physics

paper · pdf · doi:10.48550/arxiv.2308.07740

openalex publication_date 2023/08/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this article, we study the ill-posedness of the viscous nonlinear wave equation for any polynomial nonlinearity in negative Sobolev spaces. In particular, we prove a norm inflation result above the scaling critical regularity in some cases. We also show failure of C^k-continuity, for k the power of the nonlinearity, up to some regularity threshold.

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