Global-in-time Well-posedness of the One-dimensional Hydrodynamic Gross-Pitaevskii Equations without Vacuum
Fuente:
arXiv
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| Natura: | Preprint |
| Pubblicazione: |
2023
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| _version_ | 1866918219466407936 |
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| author | Wegner, Robert |
| author_facet | Wegner, Robert |
| contents | We establish global-in-time well-posedness of the one-dimensional hydrodynamic Gross-Pitaevskii equations in the absence of vacuum in $(1 + H^s) \times H^{s-1}$ with $s \geq 1$. We achieve this by a reduction via the Madelung transform to the previous global-in-time well-posedness result for the Gross-Pitaevskii equation in arXiv:1801.08386v2 [math.AP] and arXiv:2204.06293v1 [math.AP]. Our core result is a local bilipschitz equivalence between the relevant function spaces. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2303_04606 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Global-in-time Well-posedness of the One-dimensional Hydrodynamic Gross-Pitaevskii Equations without Vacuum Wegner, Robert Analysis of PDEs 35Q55, 35Q31, 37K10, 76N10 We establish global-in-time well-posedness of the one-dimensional hydrodynamic Gross-Pitaevskii equations in the absence of vacuum in $(1 + H^s) \times H^{s-1}$ with $s \geq 1$. We achieve this by a reduction via the Madelung transform to the previous global-in-time well-posedness result for the Gross-Pitaevskii equation in arXiv:1801.08386v2 [math.AP] and arXiv:2204.06293v1 [math.AP]. Our core result is a local bilipschitz equivalence between the relevant function spaces. |
| title | Global-in-time Well-posedness of the One-dimensional Hydrodynamic Gross-Pitaevskii Equations without Vacuum |
| topic | Analysis of PDEs 35Q55, 35Q31, 37K10, 76N10 |
| url | https://arxiv.org/abs/2303.04606 |