The Existence and Non-Uniqueness of Global Weak Solution to a New Integrable System in \(H^1(\mathbb {R})\)

IF 1.3 3区数学 Q2 MATHEMATICS, APPLIED

Journal of Mathematical Fluid Mechanics Pub Date : 2025-07-18 DOI:10.1007/s00021-025-00963-x

Pei Zheng, Zhaoyang Yin

引用次数: 0

Abstract

In this paper, we establish the existence of the global weak admissible solution for the Cauchy problem of a N-peakon system in the sense of \(H^1(\mathbb {R})\) space under a sign condition. Second, we claim that the global weak admissible solution for the system with the same initial data is not unique by giving a example. Finally, an image of the solutions of the above example which does not satisfy the uniqueness is given, which makes it easier to see the properties of non-uniqueness more intuitively.

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一类新的可积系统整体弱解的存在性与非唯一性 \(H^1(\mathbb {R})\)

本文在一个符号条件下，建立了\(H^1(\mathbb {R})\)空间意义上n -峰系统Cauchy问题整体弱可容许解的存在性。其次，我们通过一个例子证明了具有相同初始数据的系统的全局弱可容许解不是唯一的。最后，给出了上例不满足唯一性的解的图象，使我们更直观地看到非唯一性的性质。

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

Journal of Mathematical Fluid Mechanics 物理-力学

CiteScore

2.00

自引率

15.40%

发文量

审稿时长

>12 weeks

期刊介绍： The Journal of Mathematical Fluid Mechanics (JMFM)is a forum for the publication of high-quality peer-reviewed papers on the mathematical theory of fluid mechanics, with special regards to the Navier-Stokes equations. As an important part of that, the journal encourages papers dealing with mathematical aspects of computational theory, as well as with applications in science and engineering. The journal also publishes in related areas of mathematics that have a direct bearing on the mathematical theory of fluid mechanics. All papers will be characterized by originality and mathematical rigor. For a paper to be accepted, it is not enough that it contains original results. In fact, results should be highly relevant to the mathematical theory of fluid mechanics, and meet a wide readership.