Strichartz estimates for orthonormal systems on compact manifolds
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866909762004713472 |
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| author | Wang, Xing Zhang, An Zhang, Cheng |
| author_facet | Wang, Xing Zhang, An Zhang, Cheng |
| contents | We establish new Strichartz estimates for orthonormal systems on compact Riemannian manifolds in the case of wave, Klein-Gordon and fractional Schrödinger equations. Our results generalize the classical (single-function) Strichartz estimates on compact manifolds by Kapitanski, Burq-Gérard-Tzvetkov, Dinh, and extend the Euclidean orthonormal version by Frank-Lewin-Lieb-Seiringer, Frank-Sabin, Bez-Lee-Nakamura. On the flat torus, our new results for the Schrödinger equation cover prior work of Nakamura, which exploits the dispersive estimate of Kenig-Ponce-Vega. We achieve sharp results on compact manifolds by combining the frequency localized dispersive estimates for small time intervals with the duality principle due to Frank-Sabin. We construct examples to show these results can be saturated on the sphere, and we can improve them on the flat torus by using Bourgain-Demeter's decoupling theorem to obtain new decoupling inequalities for certain non-smooth hypersurfaces. As an application, we obtain the well-posedness of infinite systems of dispersive equations with Hartree-type nonlinearity. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_08504 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strichartz estimates for orthonormal systems on compact manifolds Wang, Xing Zhang, An Zhang, Cheng Analysis of PDEs Mathematical Physics Classical Analysis and ODEs Spectral Theory 58J45, 58J50, 58J40, 35B45 We establish new Strichartz estimates for orthonormal systems on compact Riemannian manifolds in the case of wave, Klein-Gordon and fractional Schrödinger equations. Our results generalize the classical (single-function) Strichartz estimates on compact manifolds by Kapitanski, Burq-Gérard-Tzvetkov, Dinh, and extend the Euclidean orthonormal version by Frank-Lewin-Lieb-Seiringer, Frank-Sabin, Bez-Lee-Nakamura. On the flat torus, our new results for the Schrödinger equation cover prior work of Nakamura, which exploits the dispersive estimate of Kenig-Ponce-Vega. We achieve sharp results on compact manifolds by combining the frequency localized dispersive estimates for small time intervals with the duality principle due to Frank-Sabin. We construct examples to show these results can be saturated on the sphere, and we can improve them on the flat torus by using Bourgain-Demeter's decoupling theorem to obtain new decoupling inequalities for certain non-smooth hypersurfaces. As an application, we obtain the well-posedness of infinite systems of dispersive equations with Hartree-type nonlinearity. |
| title | Strichartz estimates for orthonormal systems on compact manifolds |
| topic | Analysis of PDEs Mathematical Physics Classical Analysis and ODEs Spectral Theory 58J45, 58J50, 58J40, 35B45 |
| url | https://arxiv.org/abs/2503.08504 |