On blowup of co-rotational wave maps in odd space dimensions

TL;DR

This paper proves the asymptotic nonlinear stability of a self-similar blowup solution for co-rotational wave maps from odd-dimensional Minkowski space into spheres, advancing understanding of finite-time singularity formation in supercritical models.

Contribution

It establishes the nonlinear stability of a fundamental self-similar blowup solution in an energy-supercritical wave map model, using a novel analytical method.

Findings

Proved stability of the ground-state self-similar solution.

Demonstrated finite-time blowup behavior in the model.

Extended the analytical framework for supercritical wave maps.

Abstract

We consider co-rotational wave maps from the $(1+d)$-dimensional Minkowski space into the $d$-sphere for $d\geq 3$ odd. This is an energy-supercritical model which is known to exhibit finite-time blowup via self-similar solutions. Based on a method developed by the second author and Sch\"orkhuber, we prove the asymptotic nonlinear stability of the "ground-state" self-similar solution.