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| Format: | Preprint |
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2020
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| Online Access: | https://arxiv.org/abs/2004.08952 |
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| _version_ | 1866917283038756864 |
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| author | Choi, Brian J |
| author_facet | Choi, Brian J |
| contents | We consider the compact case of one-dimensional quantum Zakharov system, as an initial-value problem with periodic boundary conditions. We apply the Bourgain norm method to show low regularity local well-posedness for a certain class of Sobolev exponents that are sharp up to the boundary, under the condition that Schrödinger Sobolev regularity is non-negative. Using the conservation law and energy method, we show global well-posedness for sufficiently regular initial data, without any smallness assumption. Lastly we show the semi-classical limit as $ε\to 0$ on a compact time interval, whereas the quantum perturbation proves to be singular on an infinite time interval. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2004_08952 |
| institution | arXiv |
| publishDate | 2020 |
| record_format | arxiv |
| spellingShingle | Multilinear Weighted Estimates and Quantum Zakharov System Choi, Brian J Analysis of PDEs We consider the compact case of one-dimensional quantum Zakharov system, as an initial-value problem with periodic boundary conditions. We apply the Bourgain norm method to show low regularity local well-posedness for a certain class of Sobolev exponents that are sharp up to the boundary, under the condition that Schrödinger Sobolev regularity is non-negative. Using the conservation law and energy method, we show global well-posedness for sufficiently regular initial data, without any smallness assumption. Lastly we show the semi-classical limit as $ε\to 0$ on a compact time interval, whereas the quantum perturbation proves to be singular on an infinite time interval. |
| title | Multilinear Weighted Estimates and Quantum Zakharov System |
| topic | Analysis of PDEs |
| url | https://arxiv.org/abs/2004.08952 |