Classification of radial non-radiative solutions to the 5D nonlinear wave equations

2022/11/30 by Liang Li, Li, Liang, Ruipeng Shen +3
Mathematics · Physics and Astronomy · #35L05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons

paper · pdf · doi:10.48550/arxiv.2211.16907

openalex publication_date 2022/11/30 · openalex created_date 2022/12/12 · openalex updated_date 2026/07/28

Abstract

In this work we classify all radial non-radiative solutions to the 5D nonlinear wave equations with a wide range of energy critical nonlinearity. We show that such a solution always comes with two characteristic numbers. These characteristic numbers can be determined by either the radiation profile of the initial data or the asymptotic behaviour of the solution. In addition, two radial weakly non-radiative solutions with the same characteristic numbers must coincide with each other in the overlap part of their exterior regions. Finally we give a few applications of our theory on the global behaviours of solutions to the nonlinear wave equations.

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