Optimal blowup stability for three-dimensional wave maps

Donninger, Roland; Wallauch, David

doi:10.2140/apde.2025.18.895

Download this article
	For screen
	For printing

Recent Issues

The Journal

About the journal

Ethics and policies

Peer-review process

Submission guidelines

ISSN 1948-206X (online)

ISSN 2157-5045 (print)

Author index

To appear

Other MSP journals

Optimal blowup stability for three-dimensional wave maps

Roland Donninger and David Wallauch

Vol. 18 (2025), No. 4, 895–962

DOI: 10.2140/apde.2025.18.895

Abstract

We study corotational wave maps from $(1 + 3)$ -dimensional Minkowski space into the three-sphere. We establish the asymptotic stability of an explicitly known self-similar wave map under perturbations that are small in the critical Sobolev space. This is accomplished by proving Strichartz estimates for a radial wave equation with a potential in similarity coordinates. Compared to earlier work, the main novelty lies with the fact that the critical Sobolev space is of fractional order.

Keywords

nonlinear PDE, wave equations, blowup

Mathematical Subject Classification

Primary: 35L71

Secondary: 35B44, 35L15

Milestones

Received: 21 December 2022

Revised: 3 October 2023

Accepted: 21 December 2023

Published: 27 March 2025

Authors

Roland Donninger
Fakultät für Mathematik Universität Wien Vienna Austria

David Wallauch
Fakultät für Mathematik Universität Wien Vienna Austria

Open Access made possible by participating institutions via Subscribe to Open.

Vol. 18, No. 4, 2025