Extremizers for the Strichartz Inequality for a Fourth-Order Schrödinger Equation
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2022
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| _version_ | 1866917813398011904 |
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| author | Di, Boning Frier, Ryan |
| author_facet | Di, Boning Frier, Ryan |
| contents | In this paper, we consider the Strichartz inequality for a fourth-order Schrödinger equation on $\mathbb{R}^{2+1}$. We show that extremizers exist using a linear profile decomposition which follows from the endpoint version decomposition and the stationary phase method. Based on the existence of extremizers, we investigate the associated Euler-Lagrange equation to show that the extremizers have exponential decay and consequently must be analytic. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2210_06695 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Extremizers for the Strichartz Inequality for a Fourth-Order Schrödinger Equation Di, Boning Frier, Ryan Classical Analysis and ODEs Analysis of PDEs 42B10 (Primary), 35B38, 35Q41 (Secondary) In this paper, we consider the Strichartz inequality for a fourth-order Schrödinger equation on $\mathbb{R}^{2+1}$. We show that extremizers exist using a linear profile decomposition which follows from the endpoint version decomposition and the stationary phase method. Based on the existence of extremizers, we investigate the associated Euler-Lagrange equation to show that the extremizers have exponential decay and consequently must be analytic. |
| title | Extremizers for the Strichartz Inequality for a Fourth-Order Schrödinger Equation |
| topic | Classical Analysis and ODEs Analysis of PDEs 42B10 (Primary), 35B38, 35Q41 (Secondary) |
| url | https://arxiv.org/abs/2210.06695 |