Decay and Strichartz estimates for critical electromagnetic wave equations on conic manifolds
Fuente:
arXiv
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Preprint |
| Veröffentlicht: |
2025
|
| Schlagworte: | |
| Online-Zugang: | |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| _version_ | 1866911000162205696 |
|---|---|
| author | Jia, Qiuye Zhang, Junyong |
| author_facet | Jia, Qiuye Zhang, Junyong |
| contents | We establish the decay and Strichartz estimates for the wave equation with large scaling-critical electromagnetic potentials on a conical singular space $(X,g)$ with dimension $n\geq3$, where the metric $g=dr^2+r^2 h$ and $X=C(Y)=(0,\infty)\times Y$ is a product cone over the closed Riemannian manifold $(Y,h)$ with metric $h$. The decay assumption on the magnetic potentials is scaling critical and includes the decay of Coulomb type. The main technical innovation lies in proving localized pointwise estimates for the half-wave propagator by constructing a localized spectral measure, which effectively separates contributions from conjugate point pairs on $\CS$. In particular, when $Y=\mathbb{S}^{n-1}$, our results, which address the case of large critical electromagnetic potentials, extend and improve upon those in [21], which considered sufficiently decaying, and small potentials and that of [24], which considered potentials decaying faster than scaling critical ones. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2506_09635 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Decay and Strichartz estimates for critical electromagnetic wave equations on conic manifolds Jia, Qiuye Zhang, Junyong Analysis of PDEs Differential Geometry 35L05, 35B25, 37L50, 35S30, 58J60, 58J47 We establish the decay and Strichartz estimates for the wave equation with large scaling-critical electromagnetic potentials on a conical singular space $(X,g)$ with dimension $n\geq3$, where the metric $g=dr^2+r^2 h$ and $X=C(Y)=(0,\infty)\times Y$ is a product cone over the closed Riemannian manifold $(Y,h)$ with metric $h$. The decay assumption on the magnetic potentials is scaling critical and includes the decay of Coulomb type. The main technical innovation lies in proving localized pointwise estimates for the half-wave propagator by constructing a localized spectral measure, which effectively separates contributions from conjugate point pairs on $\CS$. In particular, when $Y=\mathbb{S}^{n-1}$, our results, which address the case of large critical electromagnetic potentials, extend and improve upon those in [21], which considered sufficiently decaying, and small potentials and that of [24], which considered potentials decaying faster than scaling critical ones. |
| title | Decay and Strichartz estimates for critical electromagnetic wave equations on conic manifolds |
| topic | Analysis of PDEs Differential Geometry 35L05, 35B25, 37L50, 35S30, 58J60, 58J47 |
| url | https://arxiv.org/abs/2506.09635 |