Vol. 12, No. 2, 2019

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ISSN: 1948-206X (e-only)
ISSN: 2157-5045 (print)
On the existence and stability of blowup for wave maps into a negatively curved target

Roland Donninger and Irfan Glogić

Vol. 12 (2019), No. 2, 389–416
DOI: 10.2140/apde.2019.12.389
Abstract

We consider wave maps on (1+d)-dimensional Minkowski space. For each dimension d 8 we construct a negatively curved, d-dimensional target manifold that allows for the existence of a self-similar wave map which provides a stable blowup mechanism for the corresponding Cauchy problem.

Keywords
corotational wave maps, self-similar solutions, similarity coordinates, stable blowup
Mathematical Subject Classification 2010
Primary: 35L71, 58E20, 58J45
Secondary: 35B35, 35B44
Milestones
Received: 22 May 2017
Revised: 23 November 2017
Accepted: 14 May 2018
Published: 14 August 2018
Authors
Roland Donninger
Rheinische Friedrich-Wilhelms-Universität Bonn
Mathematisches Institut
Bonn
Germany
Universität Wien
Fakultät für Mathematik
Vienna
Austria
Irfan Glogić
Department of Mathematics
The Ohio State University
Columbus, OH
United States
Universität Wien
Fakultät für Mathematik
Vienna
Austria