Strichartz estimates for a Schrödinger equation on the half-line with a Neumann boundary condition
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866916866801270784 |
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| author | Garofalo, Nicola Staffilani, Gigliola |
| author_facet | Garofalo, Nicola Staffilani, Gigliola |
| contents | In this paper we prove some new Strichartz estimates related to the Cauchy problem for the Bessel operator on the half-line and we establish a fractal version of the Tomas-Stein restriction theorem for the Hankel transform. Then we use the proved Strichartz estimates to show global in time well-posedness for a class of nonlinear $L^2_a$-critical problems, and local in time well-posedness in the sub-critical case. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2507_19998 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Strichartz estimates for a Schrödinger equation on the half-line with a Neumann boundary condition Garofalo, Nicola Staffilani, Gigliola Analysis of PDEs 35J10, 35Q41, 35Q55 In this paper we prove some new Strichartz estimates related to the Cauchy problem for the Bessel operator on the half-line and we establish a fractal version of the Tomas-Stein restriction theorem for the Hankel transform. Then we use the proved Strichartz estimates to show global in time well-posedness for a class of nonlinear $L^2_a$-critical problems, and local in time well-posedness in the sub-critical case. |
| title | Strichartz estimates for a Schrödinger equation on the half-line with a Neumann boundary condition |
| topic | Analysis of PDEs 35J10, 35Q41, 35Q55 |
| url | https://arxiv.org/abs/2507.19998 |