Local well-posedness for nonlinear Schrödinger equations on compact product manifolds
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911480277893120 |
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| author | Zhang, Yunfeng |
| author_facet | Zhang, Yunfeng |
| contents | We prove new local well-posedness results for nonlinear Schrödinger equations posed on a general product of spheres and tori, by the standard approach of multi-linear Strichartz estimates. To prove these estimates, we establish and utilize multi-linear bounds for the joint spectral projector associated to the Laplace--Beltrami operators on the individual sphere factors of the product manifold. To treat the particular case of the cubic NLS on a product of two spheres at critical regularity, we prove a sharp $L^\infty_xL^p_t$ estimate of the solution to the linear Schrödinger equation on the two-torus. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_09442 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Local well-posedness for nonlinear Schrödinger equations on compact product manifolds Zhang, Yunfeng Analysis of PDEs 35P20, 35Q55, 58J50 We prove new local well-posedness results for nonlinear Schrödinger equations posed on a general product of spheres and tori, by the standard approach of multi-linear Strichartz estimates. To prove these estimates, we establish and utilize multi-linear bounds for the joint spectral projector associated to the Laplace--Beltrami operators on the individual sphere factors of the product manifold. To treat the particular case of the cubic NLS on a product of two spheres at critical regularity, we prove a sharp $L^\infty_xL^p_t$ estimate of the solution to the linear Schrödinger equation on the two-torus. |
| title | Local well-posedness for nonlinear Schrödinger equations on compact product manifolds |
| topic | Analysis of PDEs 35P20, 35Q55, 58J50 |
| url | https://arxiv.org/abs/2503.09442 |