Orthonormal Strichartz estimates on torus and waveguide manifold and applications
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| Auteurs principaux: | , |
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| Format: | Preprint |
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2025
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| _version_ | 1866914117415075840 |
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| author | Bhimani, Divyang G. Choudhary, Subhash. R. |
| author_facet | Bhimani, Divyang G. Choudhary, Subhash. R. |
| contents | We establish new orthonormal Strichartz estimates for the fractional Schrödinger equations on torus $\mathbb T$ and waveguide manifold $\mathbb R^n\times \mathbb T^m$. We generalizes the result of Nakamura [42] on torus; while this is the first result on the waveguide manifold. The main novelty in this paper is the derivation of various kernel estimates associated to the fractional Schrödinger equations. Our kernel estimate generalizes the classical dispersive estimate on torus due to Kenig-Ponce-Vega [35]. On the other hand, we obtain new $\ell^2$ decoupling inequality for degeneracy type surfaces to treat the case of waveguide manifold; which maybe of independent interest and complements several known results. As an application, we establish local and small data global well-posednes for the Hartree equation with infinitely many particles with non-trace class initial data. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_16712 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Orthonormal Strichartz estimates on torus and waveguide manifold and applications Bhimani, Divyang G. Choudhary, Subhash. R. Analysis of PDEs 35Q55, 35B45 We establish new orthonormal Strichartz estimates for the fractional Schrödinger equations on torus $\mathbb T$ and waveguide manifold $\mathbb R^n\times \mathbb T^m$. We generalizes the result of Nakamura [42] on torus; while this is the first result on the waveguide manifold. The main novelty in this paper is the derivation of various kernel estimates associated to the fractional Schrödinger equations. Our kernel estimate generalizes the classical dispersive estimate on torus due to Kenig-Ponce-Vega [35]. On the other hand, we obtain new $\ell^2$ decoupling inequality for degeneracy type surfaces to treat the case of waveguide manifold; which maybe of independent interest and complements several known results. As an application, we establish local and small data global well-posednes for the Hartree equation with infinitely many particles with non-trace class initial data. |
| title | Orthonormal Strichartz estimates on torus and waveguide manifold and applications |
| topic | Analysis of PDEs 35Q55, 35B45 |
| url | https://arxiv.org/abs/2507.16712 |