On wave systems with antisymmetric potential in dimension d >= 4 and well-posedness for (half-)wave maps
Fuente:
arXiv
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2024
|
| Subjects: | |
| Online Access: | |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866911860089946112 |
|---|---|
| author | Farina, Silvino Reyes Schikorra, Armin |
| author_facet | Farina, Silvino Reyes Schikorra, Armin |
| contents | We prove a priori estimates for wave systems of the type \[ \partial_{tt} u - Δu = Ω\cdot du + F(u) \quad \text{in $\mathbb{R}^d \times \mathbb{R}$} \]
where $d \geq 4$ and $Ω$ is a suitable antisymmetric potential. We show that the assumptions on $Ω$ are applicable to wave- and half-wave maps, the latter by means of the Krieger-Sire reduction. We thus obtain well-posedness of those equations for small initial data in $\dot{H}^{\frac{d}{2}}(\mathbb{R}^d)$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2404_19421 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | On wave systems with antisymmetric potential in dimension d >= 4 and well-posedness for (half-)wave maps Farina, Silvino Reyes Schikorra, Armin Analysis of PDEs We prove a priori estimates for wave systems of the type \[ \partial_{tt} u - Δu = Ω\cdot du + F(u) \quad \text{in $\mathbb{R}^d \times \mathbb{R}$} \] where $d \geq 4$ and $Ω$ is a suitable antisymmetric potential. We show that the assumptions on $Ω$ are applicable to wave- and half-wave maps, the latter by means of the Krieger-Sire reduction. We thus obtain well-posedness of those equations for small initial data in $\dot{H}^{\frac{d}{2}}(\mathbb{R}^d)$. |
| title | On wave systems with antisymmetric potential in dimension d >= 4 and well-posedness for (half-)wave maps |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2404.19421 |