自治哈密顿向量场积分曲线的非唯一性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-08-11 DOI:10.57262/die035-0708-411

V. Giri, M. Sorella

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引用次数: 6

摘要

在这项工作中，我们证明了在W^{1，r}（T^d；r^d）中，当r＝4时，一个自治的哈密顿向量场的存在性，其相关的输运方程具有非唯一的正解。作为Ambrosio叠加原理的结果，我们证明了这个向量场具有非唯一的积分曲线，具有初始数据的正Lebesgue测度集，并且我们还证明了哈密顿量沿着这些积分曲线是不恒定的。

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Non-uniqueness of integral curves for autonomous Hamiltonian vector fields

In this work we prove the existence of an autonomous Hamiltonian vector field in W^{1,r}(T^d;R^d) with r=4 for which the associated transport equation has non-unique positive solutions. As a consequence of Ambrosio superposition principle, we show that this vector field has non-unique integral curves with a positive Lebesgue measure set of initial data and moreover we show that the Hamiltonian is not constant along these integral curves.

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.