Global existence for the periodic dispersive Hunter–Saxton equation

被引：0
作者：
Weikui Ye
Zhaoyang Yin
机构：
[1] Sun Yat-sen University,Department of Mathematics
[2] Macau University of Science and Technology,Faculty of Information Technology
来源：
Monatshefte für Mathematik | 2020年 / 191卷
关键词：
The periodic dispersive Hunter–Saxton equation; Local well-posedness; The Kato method; Global existence; 35A01; 35L03; 35L05; 35L60;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we study an integrable dispersive Hunter–Saxton equation in periodic domain. Firstly, we establish the local well-posedness of the Cauchy problem of the equation in Hs(S),s≥2,\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$H^s ({\mathbb {S}}), s \ge 2,$$\end{document} by applying the Kato method. Then, based on a sign-preserve property, we obtain a global existence result for the equation. Moreover, we extend the obtained result to some periodic nonlinear partial differential equations of second order of the general form.
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页码：267 / 278
页数：11
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