Acta mathematica scientia,Series B ›› 2022, Vol. 42 ›› Issue (4): 1607-1620.doi: 10.1007/s10473-022-0418-z

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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).

Abstract: We investigate the refined Carleson's problem of the free Ostrovsky equation {ut+3xu+1xu=0,u(x,0)=f(x),

where (x,t)R×R and fHs(R). We illustrate the Hausdorff dimension of the divergence set for the Ostrovsky equation α1,U(s)=12s,14s12.

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

CLC Number: 

  • 35Q53
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