关于修正Camassa-Holm方程的整体存在性

IF 1.2 2区数学 Q1 MATHEMATICS

Journal of the London Mathematical Society-Second Series Pub Date : 2025-07-08 DOI:10.1112/jlms.70232

Yiling Yang, Engui Fan, Yue Liu

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引用次数: 0

摘要

修正Camassa-Holm （mCH）方程是描述浅水波浪单向传播的一个模型。如果不知道这类拟线性评价方程在高阶Sobolev空间中的任何守恒量，获得mCH方程的全局适定性似乎是相当具有挑战性的。在本文中，我们讨论了加权Sobolev空间h2中全局解的存在性，1 (R)$ H^{2,1}(\mathbb {R})$求解mCH方程的柯西问题。证明这一结果的关键是利用基于Riemann-Hilbert问题和Cauchy问题的mCH方程的逆散射变换方法建立势系数和反射系数之间的双向性。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

On the global existence for the modified Camassa–Holm equation

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On the global existence for the modified Camassa–Holm equation

The modified Camassa–Holm (mCH) equation is a model to describe the unidirectional propagation of shallow water waves. Without knowledge of any conservation quantities in the higher order Sobolev spaces for this type of the quasi-linear evaluation equation, obtaining global well-posedness for the mCH equation appears to be quite challenging. In this paper, we address the existence of global solutions in a weighted Sobolev space $H^{2, 1} (R)$ to the Cauchy problem for the mCH equation. The key to prove this result is establish bijectivity between potential and reflection coefficient by using inverse scattering transform method based on the Riemann–Hilbert problem associated with the Cauchy problem for the mCH equation.

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来源期刊

Journal of the London Mathematical Society-Second Series 数学-数学

CiteScore

1.90

自引率

0.00%

发文量

186

审稿时长

6-12 weeks

期刊介绍： The Journal of the London Mathematical Society has been publishing leading research in a broad range of mathematical subject areas since 1926. The Journal welcomes papers on subjects of general interest that represent a significant advance in mathematical knowledge, as well as submissions that are deemed to stimulate new interest and research activity.