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

TL;DR

This paper classifies all radial non-radiative solutions to 5D nonlinear wave equations, revealing their characteristic parameters and uniqueness properties, and explores implications for the global behavior of solutions.

Contribution

It provides a complete classification of radial non-radiative solutions for 5D nonlinear wave equations with energy-critical nonlinearities, including their characteristic numbers and uniqueness results.

Findings

Solutions are characterized by two characteristic numbers.

Radial weakly non-radiative solutions with same characteristics coincide.

Applications to global behavior of solutions are demonstrated.

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.