Remarks on the derivation of the virial identity for nonlinear Schrödinger equations
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2025
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| _version_ | 1866917029316919296 |
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| author | Ikeda, Tomoyuki Machihara, Shuji Miyazaki, Hayato Ozawa, Tohru |
| author_facet | Ikeda, Tomoyuki Machihara, Shuji Miyazaki, Hayato Ozawa, Tohru |
| contents | We revisit the derivation of the virial identity for nonlinear Schrödinger equations. In \cite{O06, FM17}, several conservation laws, such as for the charge and the energy, were derived without constructing a sequence of approximate solutions. Their approach involves additional properties of solutions due to Strichartz' estimate. In this paper, we derive the virial identity without constructing the sequence of approximate solutions or employing a regularizing argument for weights, by exploiting the properties of solutions. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_18168 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Remarks on the derivation of the virial identity for nonlinear Schrödinger equations Ikeda, Tomoyuki Machihara, Shuji Miyazaki, Hayato Ozawa, Tohru Analysis of PDEs Primary 35Q55, Secondary 37K06 We revisit the derivation of the virial identity for nonlinear Schrödinger equations. In \cite{O06, FM17}, several conservation laws, such as for the charge and the energy, were derived without constructing a sequence of approximate solutions. Their approach involves additional properties of solutions due to Strichartz' estimate. In this paper, we derive the virial identity without constructing the sequence of approximate solutions or employing a regularizing argument for weights, by exploiting the properties of solutions. |
| title | Remarks on the derivation of the virial identity for nonlinear Schrödinger equations |
| topic | Analysis of PDEs Primary 35Q55, Secondary 37K06 |
| url | https://arxiv.org/abs/2510.18168 |