数学物理学报(英文版) ›› 2022, Vol. 42 ›› Issue (4): 1607-1620.doi: 10.1007/s10473-022-0418-z

• 论文 • 上一篇    下一篇

ON THE DIMENSION OF THE DIVERGENCE SET OF THE OSTROVSKY EQUATION

赵雅娟1, 李用声2, 闫威3, 闫向前3   

  1. 1. Zhengzhou University, Zhengzhou, 450001, China;
    2. South China University of Technology, Guangzhou, 510640, China;
    3. Henan Normal University, Xinxiang, 453007, China
  • 收稿日期:2020-04-15 修回日期:2021-06-04 出版日期:2022-08-25 发布日期:2022-08-23
  • 通讯作者: Yajuan ZHAO,E-mail:zhaoyj_91@zzu.edu.cn E-mail:zhaoyj_91@zzu.edu.cn
  • 基金资助:
    This work was supported by the National Natural Science Foundation of China (11571118, 11401180 and 11971356).

ON THE DIMENSION OF THE DIVERGENCE SET OF THE OSTROVSKY EQUATION

Yajuan ZHAO1, Yongsheng LI2, Wei YAN3, Xiangqian YAN3   

  1. 1. Zhengzhou University, Zhengzhou, 450001, China;
    2. South China University of Technology, Guangzhou, 510640, China;
    3. Henan Normal University, Xinxiang, 453007, China
  • Received:2020-04-15 Revised:2021-06-04 Online:2022-08-25 Published:2022-08-23
  • Contact: Yajuan ZHAO,E-mail:zhaoyj_91@zzu.edu.cn E-mail:zhaoyj_91@zzu.edu.cn
  • Supported by:
    This work was supported by the National Natural Science Foundation of China (11571118, 11401180 and 11971356).

摘要: We investigate the refined Carleson's problem of the free Ostrovsky equation \begin{equation*} \left\{ \begin{aligned} & u_t+\partial_x^3u+\partial_x^{-1}u=0,\\ & u(x,0)=f(x), \end{aligned} \right. \end{equation*} where $(x,t)\in\mathbb{R}\times\mathbb{R}$ and $f\in H^s(\mathbb{R})$. We illustrate the Hausdorff dimension of the divergence set for the Ostrovsky equation \begin{equation*} \alpha_{1,U}(s)=1-2s,\quad \frac{1}{4}\leq s\leq\frac{1}{2}. \end{equation*}

关键词: Free Ostrovsky equation, Hausdorff dimension, divergence set

Abstract: We investigate the refined Carleson's problem of the free Ostrovsky equation \begin{equation*} \left\{ \begin{aligned} & u_t+\partial_x^3u+\partial_x^{-1}u=0,\\ & u(x,0)=f(x), \end{aligned} \right. \end{equation*} where $(x,t)\in\mathbb{R}\times\mathbb{R}$ and $f\in H^s(\mathbb{R})$. We illustrate the Hausdorff dimension of the divergence set for the Ostrovsky equation \begin{equation*} \alpha_{1,U}(s)=1-2s,\quad \frac{1}{4}\leq s\leq\frac{1}{2}. \end{equation*}

Key words: Free Ostrovsky equation, Hausdorff dimension, divergence set

中图分类号: 

  • 35Q53