Non-uniqueness of integral curves for autonomous Hamiltonian vector fields

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

引用次数: 6

Abstract

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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自治哈密顿向量场积分曲线的非唯一性

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。

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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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

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