Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2026
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2604.15947 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866915942057902080 |
|---|---|
| author | Lafontaine, David Laurent, Camille |
| author_facet | Lafontaine, David Laurent, Camille |
| contents | We prove scattering for the defocusing energy-critical non-linear wave equation with Dirichlet boundary conditions outside two strictly convex obstacles in dimension three. This is the first large data scattering result for such an equation in the presence of trapped trajectories. Our result is in fact more general and can be used as a black box in other geometries. More precisely, under the assumptions that the corresponding linear wave equation satisfies global Strichartz estimates, that the domain is weakly non-trapping and that trajectories do not reconcentrate, we show linear and nonlinear profile decompositions in infinite time. This implies scattering under the rigidity assumption that the only compact-flow solution is the trivial one. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2604_15947 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | On scattering and profile decomposition for critical nonlinear waves outside weakly trapping obstacles Lafontaine, David Laurent, Camille Analysis of PDEs We prove scattering for the defocusing energy-critical non-linear wave equation with Dirichlet boundary conditions outside two strictly convex obstacles in dimension three. This is the first large data scattering result for such an equation in the presence of trapped trajectories. Our result is in fact more general and can be used as a black box in other geometries. More precisely, under the assumptions that the corresponding linear wave equation satisfies global Strichartz estimates, that the domain is weakly non-trapping and that trajectories do not reconcentrate, we show linear and nonlinear profile decompositions in infinite time. This implies scattering under the rigidity assumption that the only compact-flow solution is the trivial one. |
| title | On scattering and profile decomposition for critical nonlinear waves outside weakly trapping obstacles |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2604.15947 |