Wave equation on general noncompact symmetric spaces
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2020
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| _version_ | 1866910661411340288 |
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| author | Anker, Jean-Philippe Zhang, Hong-Wei |
| author_facet | Anker, Jean-Philippe Zhang, Hong-Wei |
| contents | We establish sharp pointwise kernel estimates and dispersive properties for the wave equation on noncompact symmetric spaces of general rank. This is achieved by combining the stationary phase method and the Hadamard parametrix, and in particular, by introducing a subtle spectral decomposition, which allows us to overcome a well-known difficulty in higher rank analysis, namely the fact that the Plancherel density is not a differential symbol in general. As consequences, we deduce the Strichartz inequality for a large family of admissible pairs and prove global well-posedness results for the corresponding semilinear equation with low regularity data as on hyperbolic spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2010_08467 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Wave equation on general noncompact symmetric spaces Anker, Jean-Philippe Zhang, Hong-Wei Analysis of PDEs 22E30, 35L05, 43A85, 43A90 We establish sharp pointwise kernel estimates and dispersive properties for the wave equation on noncompact symmetric spaces of general rank. This is achieved by combining the stationary phase method and the Hadamard parametrix, and in particular, by introducing a subtle spectral decomposition, which allows us to overcome a well-known difficulty in higher rank analysis, namely the fact that the Plancherel density is not a differential symbol in general. As consequences, we deduce the Strichartz inequality for a large family of admissible pairs and prove global well-posedness results for the corresponding semilinear equation with low regularity data as on hyperbolic spaces. |
| title | Wave equation on general noncompact symmetric spaces |
| topic | Analysis of PDEs 22E30, 35L05, 43A85, 43A90 |
| url | https://arxiv.org/abs/2010.08467 |