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.

25 pages

References in corpus (2)

• Mode stability of self-similar wave maps in higher dimensions
• Threshold for blowup for equivariant wave maps in higher dimensions

Cited by in corpus (2)

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