Radiation fields and non-radiative solutions to the energy sub-critical wave equations

2022/06/25 by Liang Li, Li, Liang, Ruipeng Shen +3
Mathematics · Physics and Astronomy · #35L05 #35L71 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2206.12544

openalex publication_date 2022/06/25 · openalex created_date 2022/06/30 · openalex updated_date 2026/07/28

Abstract

Radiation field and channel of energy method have become important tools in the study of nonlinear wave equations in recent years. In this work we give basic theory of radiation fields of free waves in the energy sub-critical case. We also show that the asymptotic behaviours of non-radiative solutions to a wide range of non-linear wave equations resemble those of non-radiative free waves. Our theory is completely given in the critical Sobolev spaces of the corresponding nonlinear wave equation and avoids any assumption on the energy of the solutions.

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