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

IF 1.7 3区数学 Q2 MATHEMATICS, APPLIED

Zeitschrift fur Angewandte Mathematik und Physik Pub Date : 2023-09-15 DOI:10.1007/s00033-023-02089-4

Robert Wegner

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引用次数: 0

Abstract

Abstract We establish global-in-time well-posedness of the one-dimensional hydrodynamic Gross–Pitaevskii equations in the absence of vacuum in $$(1 + H^s) \times H^{s-1}$$ ( 1 + H s ) × H s - 1 with $$s \ge 1$$ 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.

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无真空的一维水动力Gross-Pitaevskii方程的全局时适性

摘要建立了无真空条件下$$(1 + H^s) \times H^{s-1}$$ (1 + H s) × H s - 1 ($$s \ge 1$$ s≥1)下一维水动力Gross-Pitaevskii方程的全局时适性。我们通过Madelung变换将之前的Gross-Pitaevskii方程的全局时间适定性结果简化到Koch和Liao (Adv Math 377, 2021;Adv数学420,2023)。我们的核心结果是相关函数空间的局部bilipschitz等价，它使结果在两个方程之间传递。

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来源期刊

Zeitschrift fur Angewandte Mathematik und Physik 数学-应用数学

CiteScore

2.90

自引率

10.00%

发文量

216

审稿时长

6-12 weeks

期刊介绍： The Journal of Applied Mathematics and Physics (ZAMP) publishes papers of high scientific quality in Fluid Mechanics, Mechanics of Solids and Differential Equations/Applied Mathematics. A paper will be considered for publication if at least one of the following conditions is fulfilled: The paper includes results or discussions which can be considered original and highly interesting. The paper presents a new method. The author reviews a problem or a class of problems with such profound insight that further research is encouraged. The readers of ZAMP will find not only articles in their own special field but also original work in neighbouring domains. This will lead to an exchange of ideas; concepts and methods which have proven to be successful in one field may well be useful to other areas. ZAMP attempts to publish articles reasonably quickly. Longer papers are published in the section "Original Papers", shorter ones may appear under "Brief Reports" where publication is particularly rapid. The journal includes a "Book Review" section and provides information on activities (such as upcoming symposia, meetings or special courses) which are of interest to its readers.