Uniqueness of solutions for the logarithmic Schrödinger equation
Fuente:
arXiv
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| Format: | Preprint |
| Veröffentlicht: |
2025
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| _version_ | 1866912295291977728 |
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| author | Hayashi, Masayuki |
| author_facet | Hayashi, Masayuki |
| contents | We consider the Cauchy problem for the logarithmic Schrödinger equation and prove uniqueness of weak $H^s(\mathbb{R}^d)$ solutions for $s\in(0,1)$, which improves on the previous uniqueness result in $H^1(\mathbb{R}^d)$. The proof is achieved by combining a nontrivial use of integral equations, local smoothing estimates, and quantitative estimates of the sublinear effect of the nonlinearity, based on the localization argument. We also study uniqueness on the torus and uniqueness of the equation perturbed by pure power nonlinearities. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2503_20531 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Uniqueness of solutions for the logarithmic Schrödinger equation Hayashi, Masayuki Analysis of PDEs We consider the Cauchy problem for the logarithmic Schrödinger equation and prove uniqueness of weak $H^s(\mathbb{R}^d)$ solutions for $s\in(0,1)$, which improves on the previous uniqueness result in $H^1(\mathbb{R}^d)$. The proof is achieved by combining a nontrivial use of integral equations, local smoothing estimates, and quantitative estimates of the sublinear effect of the nonlinearity, based on the localization argument. We also study uniqueness on the torus and uniqueness of the equation perturbed by pure power nonlinearities. |
| title | Uniqueness of solutions for the logarithmic Schrödinger equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2503.20531 |