数学物理学报(英文版) ›› 2025, Vol. 45 ›› Issue (3): 937-950.doi: 10.1007/s10473-025-0311-7

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ON SINGULARITY FORMATION FOR 3-$D$ ZERO PRESSURE FLOW

Wei HUO   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • 收稿日期:2023-09-18 修回日期:2024-07-27 出版日期:2025-05-25 发布日期:2025-09-30

ON SINGULARITY FORMATION FOR 3-$D$ ZERO PRESSURE FLOW

Wei HUO   

  1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China
  • Received:2023-09-18 Revised:2024-07-27 Online:2025-05-25 Published:2025-09-30
  • About author:Wei HUO, E-mail : huowei@whu.edu.cn
  • Supported by:
    National Key R & D Program of China (2021YFA1001700), the NSFC (12071360) and the Fundamental Research Funds for the Central Universities in China.

摘要: We provide the breakdown mechanism of pressureless gases when the initial vorticity is zero. In other words, the maximum norm of the divergence and $\Vert u\Vert_{H^{\frac{1}{2}}}$ control the breakdown of the solution. Then we show that the solution must blow up for certain initial data in both non-relativistic and relativistic settings.

关键词: pressureless gases, singularity, relativity

Abstract: We provide the breakdown mechanism of pressureless gases when the initial vorticity is zero. In other words, the maximum norm of the divergence and $\Vert u\Vert_{H^{\frac{1}{2}}}$ control the breakdown of the solution. Then we show that the solution must blow up for certain initial data in both non-relativistic and relativistic settings.

Key words: pressureless gases, singularity, relativity

中图分类号: 

  • 35L65