Interpolation scattering for wave equations with singular potentials and singular data
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866917351955365888 |
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| author | Xuan, Pham Truong |
| author_facet | Xuan, Pham Truong |
| contents | In this paper we investigate a construction of scattering for wave-type equations with singular potentials on the whole space $\mathbb{R}^n$ in a framework of weak-$L^p$ spaces. First, we use an Yamazaki-type estimate for wave groups on Lorentz spaces and fixed point arguments to prove the global well-posedness for wave-type equations on weak-$L^p$ spaces. Then, we provide a corresponding scattering results in such singular framework. Finally, we use also the dispersive estimates to establish the polynomial stability and improve the decay of scattering in weak-$L^p$ spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2409_07867 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Interpolation scattering for wave equations with singular potentials and singular data Xuan, Pham Truong Analysis of PDEs Mathematical Physics Functional Analysis In this paper we investigate a construction of scattering for wave-type equations with singular potentials on the whole space $\mathbb{R}^n$ in a framework of weak-$L^p$ spaces. First, we use an Yamazaki-type estimate for wave groups on Lorentz spaces and fixed point arguments to prove the global well-posedness for wave-type equations on weak-$L^p$ spaces. Then, we provide a corresponding scattering results in such singular framework. Finally, we use also the dispersive estimates to establish the polynomial stability and improve the decay of scattering in weak-$L^p$ spaces. |
| title | Interpolation scattering for wave equations with singular potentials and singular data |
| topic | Analysis of PDEs Mathematical Physics Functional Analysis |
| url | https://arxiv.org/abs/2409.07867 |