The Radial Wave Operator in Similarity Coordinates

TL;DR

This paper develops a rigorous mathematical framework to analyze the radial wave equation in similarity coordinates and applies it to study the linear stability of a fundamental self-similar solution with focusing nonlinearity.

Contribution

It introduces a new functional analytic setting for the radial wave equation in similarity coordinates and applies it to stability analysis of self-similar solutions.

Findings

Established a rigorous framework for the radial wave equation in similarity coordinates.

Analyzed the linear stability of a key self-similar solution.

Provided insights into the behavior of solutions with focusing power nonlinearity.

Abstract

We present a rigorous functional analytic setting to study the radial wave equation in similarity coordinates. As an application we analyse linear stability of the fundamental self--similar solution of the wave equation with a focusing power nonlinearity.