对数薛定谔方程的考希问题再探讨

IF 1.4 3区物理与天体物理 Q2 PHYSICS, MATHEMATICAL Annales Henri Poincaré Pub Date : 2024-06-25 DOI:10.1007/s00023-024-01460-z

Masayuki Hayashi, Tohru Ozawa

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引用次数: 0

摘要

我们重温了对数薛定谔方程的考奇问题，并在\(H^1\)、能量空间和\(H^2\)-能量空间中构造了强解。这些解是以一种不依赖于紧凑性论证的构造性方式提供的，即近似解的序列在一个完整的函数空间中形成一个考希序列，然后证明实际收敛是在强意义上的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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The Cauchy Problem for the Logarithmic Schrödinger Equation Revisited

We revisit the Cauchy problem for the logarithmic Schrödinger equation and construct strong solutions in \(H^1\), the energy space, and the \(H^2\)-energy space. The solutions are provided in a constructive way, which does not rely on compactness arguments, that a sequence of approximate solutions forms a Cauchy sequence in a complete function space and then actual convergence is shown to be in a strong sense.

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来源期刊

Annales Henri Poincaré 物理-物理：粒子与场物理

CiteScore

3.00

自引率

6.70%

发文量

108

审稿时长

6-12 weeks

期刊介绍： The two journals Annales de l''Institut Henri Poincaré, physique théorique and Helvetica Physical Acta merged into a single new journal under the name Annales Henri Poincaré - A Journal of Theoretical and Mathematical Physics edited jointly by the Institut Henri Poincaré and by the Swiss Physical Society. The goal of the journal is to serve the international scientific community in theoretical and mathematical physics by collecting and publishing original research papers meeting the highest professional standards in the field. The emphasis will be on analytical theoretical and mathematical physics in a broad sense.