The Zakharov system in dimension $d \geqslant 4$
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2019
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| _version_ | 1866916150641688576 |
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| author | Candy, Timothy Herr, Sebastian Nakanishi, Kenji |
| author_facet | Candy, Timothy Herr, Sebastian Nakanishi, Kenji |
| contents | The sharp range of Sobolev spaces is determined in which the Cauchy problem for the classical Zakharov system is well-posed, which includes existence of solutions, uniqueness, persistence of initial regularity, and real-analytic dependence on the initial data. In addition, under a condition on the data for the Schrödinger equation at the lowest admissible regularity, global well-posedness and scattering is proved. The results cover energy-critical and energy-supercritical dimensions $d \geqslant 4$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1912_05820 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | The Zakharov system in dimension $d \geqslant 4$ Candy, Timothy Herr, Sebastian Nakanishi, Kenji Analysis of PDEs The sharp range of Sobolev spaces is determined in which the Cauchy problem for the classical Zakharov system is well-posed, which includes existence of solutions, uniqueness, persistence of initial regularity, and real-analytic dependence on the initial data. In addition, under a condition on the data for the Schrödinger equation at the lowest admissible regularity, global well-posedness and scattering is proved. The results cover energy-critical and energy-supercritical dimensions $d \geqslant 4$. |
| title | The Zakharov system in dimension $d \geqslant 4$ |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/1912.05820 |