Vol. 12, No. 2, 2019

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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

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.

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