L²-blowup estimates of the wave equation and its application to local energy decay

2021/11/03 by Ryo Ikehata, Ikehata, Ryo · 2 citations
Engineering · Mathematics · #35B40 #35C20 #35L05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods in inverse problems #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2111.02031

openalex publication_date 2021/11/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the Cauchy problems in the whole space for the wave equation with a weighted L¹-initial data. We first derive sharp infinite time blowup estimates of the L²-norm of solutions in the one and two dimensional cases. Then, we apply it to the local energy decay estimates for n = 2, which is not studied so completely when the 0-th moment of the initial velocity does not vanish. The idea to derive them is strongly inspired from a technique used in the author's previous papers.

Cited by

• Fast energy decay for 2-D wave equation with localized damping near spatial infinity
• Local energy decay for 2-D wave equations with variable coefficients

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