On the stability of self-similar solutions to nonlinear wave equations

TL;DR

This paper proves the mode and nonlinear stability of a self-similar blowup solution to an energy-supercritical Yang-Mills equation, offering a rigorous approach applicable to similar nonlinear wave problems.

Contribution

It provides the first rigorous proof of nonlinear stability for a self-similar blowup in a supercritical wave equation, extending previous mode stability results.

Findings

Mode stability of the self-similar solution established

Nonlinear stability proven for large initial data

Method applicable to other nonlinear wave equations

Abstract

We consider an explicit self-similar solution to an energy-supercritical Yang-Mills equation and prove its mode stability. Based on earlier work by one of the authors, we obtain a fully rigorous proof of the nonlinear stability of the self-similar blowup profile. This is a large-data result for a supercritical wave equation. Our method is broadly applicable and provides a general approach to stability problems related to self-similar solutions of nonlinear wave equations.