Well-posedness and scattering for wave equations on hyperbolic spaces with singular data
Fuente:
arXiv
Salvato in:
| Autori principali: | , |
|---|---|
| Natura: | Preprint |
| Pubblicazione: |
2023
|
| Soggetti: | |
| Accesso online: | |
| Tags: |
Aggiungi Tag
Nessun Tag, puoi essere il primo ad aggiungerne!!
|
| _version_ | 1866917722447675392 |
|---|---|
| author | Ferreira, Lucas C. F. Xuan, Pham Truong |
| author_facet | Ferreira, Lucas C. F. Xuan, Pham Truong |
| contents | We consider the wave and Klein-Gordon equations on the real hyperbolic space $\mathbb{H}^{n}$ ($n \geq2$) in a framework based on weak-$L^{p}$ spaces. First, we establish dispersive estimates on Lorentz spaces in the context of $\mathbb{H}^{n}$. Then, employing those estimates, we prove global well-posedness of solutions and an exponential asymptotic stability property. Moreover, we develop a scattering theory and construct wave operators in such singular framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_06291 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Well-posedness and scattering for wave equations on hyperbolic spaces with singular data Ferreira, Lucas C. F. Xuan, Pham Truong Analysis of PDEs Mathematical Physics Differential Geometry Functional Analysis We consider the wave and Klein-Gordon equations on the real hyperbolic space $\mathbb{H}^{n}$ ($n \geq2$) in a framework based on weak-$L^{p}$ spaces. First, we establish dispersive estimates on Lorentz spaces in the context of $\mathbb{H}^{n}$. Then, employing those estimates, we prove global well-posedness of solutions and an exponential asymptotic stability property. Moreover, we develop a scattering theory and construct wave operators in such singular framework. |
| title | Well-posedness and scattering for wave equations on hyperbolic spaces with singular data |
| topic | Analysis of PDEs Mathematical Physics Differential Geometry Functional Analysis |
| url | https://arxiv.org/abs/2303.06291 |