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<p>We investigate the partial regularity of suitable weak solutions to the three-dimensional (3D) fractional Navier–Stokes equations, where the dissipation is given as a fractional Laplacian (−Δ)<sup><i>α</i></sup> for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\alpha \in ({3\over 4},1)\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mi>α</mi> <mo>∈</mo> <mo stretchy="false">(</mo> <mrow> <mfrac> <mn>3</mn> <mn>4</mn> </mfrac> </mrow> <mo>,</mo> <mn>1</mn> <mo stretchy="false">)</mo> </math></EquationSource> </InlineEquation>, in terms of the velocity gradient. Our result represents an enhanced version of the Caffarelli–Kohn–Nirenberg criterion and extends the recent result by Tang and Yu [<CitationRef CitationID="CR23">23</CitationRef>].</p>

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On the local regularity of suitable weak solutions to the 3D fractional Navier–Stokes equations

  • 期刊论文

  • 发表日期：

    2025年12月3日

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  • Qiao Liu

摘要

We investigate the partial regularity of suitable weak solutions to the three-dimensional (3D) fractional Navier–Stokes equations, where the dissipation is given as a fractional Laplacian (−Δ)α for \(\alpha \in ({3\over 4},1)\) α ∈ ( 3 4 , 1 ) , in terms of the velocity gradient. Our result represents an enhanced version of the Caffarelli–Kohn–Nirenberg criterion and extends the recent result by Tang and Yu [23].