On the existence and stability of blowup for wave maps into a negatively curved target

Abstract

We consider wave maps on $(1+d)$-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.

arXiv comment25 pages

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Cited by in corpus (2)

• Co-dimension one stable blowup for the supercritical cubic wave equation
• Optimal blowup stability for three-dimensional wave maps