Mode stability of self-similar wave maps in higher dimensions

TL;DR

This paper proves the mode stability of explicit self-similar wave maps in higher dimensions, confirming their robustness and potential relevance in the study of wave map dynamics.

Contribution

The paper provides a rigorous proof of mode stability for the explicit self-similar wave maps discovered by Bizoń and Biernat in dimensions four and higher.

Findings

Confirmed mode stability of self-similar wave maps in dimensions d≥4

Validated the robustness of explicit self-similar solutions

Contributed to understanding wave map stability in higher dimensions

Abstract

We consider co-rotational wave maps from Minkowski space in $d+1$ dimensions to the $d$-sphere. Recently, Bizo\'n and Biernat found explicit self-similar solutions for each dimension $d\geq 4$. We give a rigorous proof for the mode stability of these self-similar wave maps.