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<p>This paper studies blow-up criteria for the 3D Navier-Stokes equations with horizontal dissipation. By using delicate energy estimate, we prove that if two components of the velocity field belong to some Lorentz spaces in both time and spatial directions, then the strong solution exists globally.</p>

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New Blow-up Criteria for the 3D Navier-Stokes Equations with Horizontal Dissipation

  • 期刊论文

  • 发表日期：

    2026年4月22日

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  • Zhouyu Li,
  • Wenjuan Liu

摘要

This paper studies blow-up criteria for the 3D Navier-Stokes equations with horizontal dissipation. By using delicate energy estimate, we prove that if two components of the velocity field belong to some Lorentz spaces in both time and spatial directions, then the strong solution exists globally.