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

## TL;DR

This paper constructs specific negatively curved target manifolds for wave maps in dimensions 8 and higher, demonstrating the existence of stable blowup solutions that serve as a blowup mechanism in the Cauchy problem.

## Contribution

It introduces new negatively curved target manifolds enabling stable blowup solutions for wave maps in high dimensions.

## Key findings

- Existence of self-similar wave maps in dimensions ≥8
- Construction of negatively curved target manifolds
- Identification of stable blowup mechanisms

## Abstract

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