Global-in-time well-posedness of the one-dimensional hydrodynamic Gross–Pitaevskii equations without vacuum
Abstract:
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 $s\ge1$. 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 [17, 18]. Our core result is a local bilipschitz equivalence between the relevant function spaces.
| Zugehörige Institution(en) am KIT | Institut für Analysis (IANA) Sonderforschungsbereich 1173 (SFB 1173) |
| Publikationstyp | Forschungsbericht/Preprint |
| Publikationsmonat/-jahr | 03.2023 |
| Sprache | Englisch |
| Identifikator | ISSN: 2365-662X KITopen-ID: 1000156897 |
| Verlag | KIT, Karlsruhe |
| Umfang | 29 S. |
| Serie | CRC 1173 Preprint ; 2023/10 |
| Projektinformation | SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019) |
| Externe Relationen | Siehe auch |
| Schlagwörter | Gross–Pitaevskii equation, Madelung transform, Madelung equations, Euler–Korteweg system, nonzero boundary condition, global well-posedness |