Threshold for blowup for equivariant wave maps in higher dimensions

Abstract

We consider equivariant wave maps from ${\mathbb{R}}^{d+1}$ to ${\mathbb{S}}^d$ in supercritical dimensions $3\le d\le 6$. Using mixed numerical and analytic methods, we show that the threshold of blowup is given by the codimension-one stable manifold of a self-similar solution with one instability.

arXiv comment11 pages, 3 figures

References in corpus (3)

• Dispersion and collapse of wave maps
• Equivariant self-similar wave maps from Minkowski spacetime into 3-sphere
• Generic self-similar blowup for equivariant wave maps and Yang-Mills fields in higher dimensions

Cited by in corpus (5)

• Threshold for blowup for the supercritical cubic wave equation
• On the existence and stability of blowup for wave maps into a negatively curved target
• On blowup for the supercritical quadratic wave equation
• Co-dimension one stable blowup for the supercritical cubic wave equation
• On blowup of co-rotational wave maps in odd space dimensions