Global-in-time well-posedness of the one-dimensional hydrodynamic Gross–Pitaevskii equations without vacuum

被引：0
|
作者：
Wegner R. [1 ]
机构：
[1] Institute for Analysis, Karlsruhe Institute of Technology, Englerstrasse 2, Karlsruhe
来源：
Zeitschrift fur Angewandte Mathematik und Physik | 2023年 / 74卷 / 05期
关键词：
Euler–Korteweg system; Global well-posedness; Gross–Pitaevskii equation; Madelung equations; Madelung transform; Nonzero boundary condition;
D O I：
10.1007/s00033-023-02089-4
中图分类号：
学科分类号：
摘要：
We establish global-in-time well-posedness of the one-dimensional hydrodynamic Gross–Pitaevskii equations in the absence of vacuum in (1 + Hs) × Hs-1 with s≥ 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 Koch and Liao (Adv Math 377, 2021; Adv Math 420, 2023). Our core result is a local bilipschitz equivalence of the relevant function spaces, which enables the transfer of results between the two equations. © 2023, The Author(s).
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