arXiv
Open Access
2023
Global-in-time Well-posedness of the One-dimensional Hydrodynamic Gross-Pitaevskii Equations without Vacuum
Robert Wegner
Abstrak
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.
Topik & Kata Kunci
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Robert Wegner
Akses Cepat
Informasi Jurnal
- Tahun Terbit
- 2023
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- en
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- arXiv
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- Open Access ✓