#### 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
##### Abstract

We consider wave maps on $\left(1+d\right)$-dimensional Minkowski space. For each dimension $d\ge 8$ 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