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<p>We investigate the partial regularity of suitable weak solutions to the three-dimensional (3d) hyperdissipative Navier–Stokes equations in terms of the velocity gradient. Our result can be regarded as a generalization of the partial regularity criterion by Colombo et al. (Commun Pure Appl Math LXXIII:0609–0663, 2022). Additionally, we establish an upper bound for the number of singular points at any fixed time.</p>

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Partial Regularity and Number of Singular Points of the Hyperdissipative Navier–Stokes Equations

  • 期刊论文

  • 发表日期：

    2026年1月9日

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  • Qiao Liu

摘要

We investigate the partial regularity of suitable weak solutions to the three-dimensional (3d) hyperdissipative Navier–Stokes equations in terms of the velocity gradient. Our result can be regarded as a generalization of the partial regularity criterion by Colombo et al. (Commun Pure Appl Math LXXIII:0609–0663, 2022). Additionally, we establish an upper bound for the number of singular points at any fixed time.