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On the Dimension of the Divergence Set of the Ostrovsky Equation

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Abstract

We investigate the refined Carleson’s problem of the free Ostrovsky equation

$$\left\{ {\matrix{{{u_t} + \partial _x^3u + \partial _x^{ - 1}u = 0,} \hfill \cr {u(x,0) = f(x),} \hfill \cr } } \right.$$

where (x, t) ∈ ℝ × ℝ and f ∈ Hs(ℝ). We illustrate the Hausdorff dimension of the divergence set for the Ostrovsky equation

$${\alpha _{1,U}}(s) = 1 - 2s,\,\,\,\,\,\,{1 \over 4} \le s \le {1 \over 2}.$$

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Authors and Affiliations

  1. Zhengzhou University, Zhengzhou, 450001, China

    Yajuan Zhao

  2. South China University of Technology, Guangzhou, 510640, China

    Yongsheng Li

  3. Henan Normal University, Xinxiang, 453007, China

    Wei Yan & Xiangqian Yan

Authors
  1. Yajuan Zhao
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  2. Yongsheng Li
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  3. Wei Yan
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  4. Xiangqian Yan
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Corresponding author

Correspondence to Yajuan Zhao.

Additional information

This work was supported by the National Natural Science Foundation of China (11571118, 11401180 and 11971356).

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Zhao, Y., Li, Y., Yan, W. et al. On the Dimension of the Divergence Set of the Ostrovsky Equation. Acta Math Sci 42, 1607–1620 (2022). https://doi.org/10.1007/s10473-022-0418-z

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  • DOI: https://doi.org/10.1007/s10473-022-0418-z

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