Smooth finite time singularity formation without quantization
Fuente:
arXiv
Saved in:
| Main Author: | |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866912967854915584 |
|---|---|
| author | Kadar, Istvan |
| author_facet | Kadar, Istvan |
| contents | We revisit the finite time singularity formation of Krieger-Schlag-Tataru [KST09] for the focusing energy critical wave equation in $\mathbb{R}^{3+1}$ from a geometric singular-analytic point of view, following Hintz [Hintz23]. We construct $C^{ν/2-}$ regular approximate solutions that settle down to multiple solitons, shrinking at a rate $t^ν$ with $ν>1$, and approaching the origin on different geodesics $\{x=zt\}$. By fine tuning the velocities, sizes and signs of the solitons, we are able to construct smooth ansätze with any $ν>8$. Using robust energy estimates, the ansätze are corrected to exact solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_14985 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Smooth finite time singularity formation without quantization Kadar, Istvan Analysis of PDEs We revisit the finite time singularity formation of Krieger-Schlag-Tataru [KST09] for the focusing energy critical wave equation in $\mathbb{R}^{3+1}$ from a geometric singular-analytic point of view, following Hintz [Hintz23]. We construct $C^{ν/2-}$ regular approximate solutions that settle down to multiple solitons, shrinking at a rate $t^ν$ with $ν>1$, and approaching the origin on different geodesics $\{x=zt\}$. By fine tuning the velocities, sizes and signs of the solitons, we are able to construct smooth ansätze with any $ν>8$. Using robust energy estimates, the ansätze are corrected to exact solutions. |
| title | Smooth finite time singularity formation without quantization |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2603.14985 |