Well-posedness for a generalized derivative nonlinear Schrödinger equation
Fuente:
arXiv
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| Autores principales: | , |
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| Formato: | Preprint |
| Publicado: |
2016
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| Materias: | |
| Acceso en línea: | |
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| _version_ | 1866929731975249920 |
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| author | Hayashi, Masayuki Ozawa, Tohru |
| author_facet | Hayashi, Masayuki Ozawa, Tohru |
| contents | We study the Cauchy problem for a generalized derivative nonlinear Schrödinger equation with the Dirichlet boundary condition. We establish the local well-posedness results in the Sobolev spaces $H^1$ and $H^2$. Solutions are constructed as a limit of approximate solutions by a method independent of a compactness argument. We also discuss the global existence of solutions in the energy space $H^1$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1601_04167 |
| institution | arXiv |
| publishDate | 2016 |
| record_format | arxiv |
| spellingShingle | Well-posedness for a generalized derivative nonlinear Schrödinger equation Hayashi, Masayuki Ozawa, Tohru Analysis of PDEs We study the Cauchy problem for a generalized derivative nonlinear Schrödinger equation with the Dirichlet boundary condition. We establish the local well-posedness results in the Sobolev spaces $H^1$ and $H^2$. Solutions are constructed as a limit of approximate solutions by a method independent of a compactness argument. We also discuss the global existence of solutions in the energy space $H^1$. |
| title | Well-posedness for a generalized derivative nonlinear Schrödinger equation |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1601.04167 |