Global and blow-up solutions for a non-local integrable equation with applications to geometry
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866908678064439296 |
|---|---|
| author | Mutlubas, Nilay Duruk Freire, Igor Leite |
| author_facet | Mutlubas, Nilay Duruk Freire, Igor Leite |
| contents | We establish the global existence of higher-order Sobolev solutions for a non-local integrable evolution equation arising in the study of pseudospherical surfaces and non-linear wave propagation. Under a natural assumption on the initial momentum, we prove that the solution remains globally regular in arbitrary finite-order Sobolev spaces. The proof relies on an inductive energy method involving a hierarchy of functional estimates and applies to both the periodic and non-periodic settings. We determine a criterion for the existence of blow-up solutions. The consequences of these qualitative properties of the solutions on Riemannian surfaces determined by the solutions of the equation are investigated. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2505_12232 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Global and blow-up solutions for a non-local integrable equation with applications to geometry Mutlubas, Nilay Duruk Freire, Igor Leite Analysis of PDEs 35B45, 37K10 We establish the global existence of higher-order Sobolev solutions for a non-local integrable evolution equation arising in the study of pseudospherical surfaces and non-linear wave propagation. Under a natural assumption on the initial momentum, we prove that the solution remains globally regular in arbitrary finite-order Sobolev spaces. The proof relies on an inductive energy method involving a hierarchy of functional estimates and applies to both the periodic and non-periodic settings. We determine a criterion for the existence of blow-up solutions. The consequences of these qualitative properties of the solutions on Riemannian surfaces determined by the solutions of the equation are investigated. |
| title | Global and blow-up solutions for a non-local integrable equation with applications to geometry |
| topic | Analysis of PDEs 35B45, 37K10 |
| url | https://arxiv.org/abs/2505.12232 |