Sobolev norms of $L^2$-solutions to NLS
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866912106178150400 |
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| author | Bessonov, Roman V. Denisov, Sergey A. |
| author_facet | Bessonov, Roman V. Denisov, Sergey A. |
| contents | We apply inverse spectral theory to study Sobolev norms of solutions to the nonlinear Schrodinger equation. For initial datum $q_0\in L^2(\mathbb{R})$ and $s\in [-1,0]$, we prove that there exists a conserved quantity that is equivalent to $H^s(\mathbb{R})$-norm of the solution. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2211_07051 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | Sobolev norms of $L^2$-solutions to NLS Bessonov, Roman V. Denisov, Sergey A. Analysis of PDEs Mathematical Physics Spectral Theory 35Q55 We apply inverse spectral theory to study Sobolev norms of solutions to the nonlinear Schrodinger equation. For initial datum $q_0\in L^2(\mathbb{R})$ and $s\in [-1,0]$, we prove that there exists a conserved quantity that is equivalent to $H^s(\mathbb{R})$-norm of the solution. |
| title | Sobolev norms of $L^2$-solutions to NLS |
| topic | Analysis of PDEs Mathematical Physics Spectral Theory 35Q55 |
| url | https://arxiv.org/abs/2211.07051 |