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<p>In this paper, we investigate the partial regularity of the suitable weak solution to three-dimensional incompressible Navier–Stokes–Landau–Lifshitz system and establish <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="33_2025_2537_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> </InlineEquation>-regularity criteria. As an application of <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="33_2025_2537_Article_IEq1.gif" Format="GIF" Height="10" Rendition="HTML" Resolution="72" Type="Linedraw" Width="11" /> </InlineMediaObject> <EquationSource Format="TEX">\(\varepsilon \)</EquationSource> <EquationSource Format="MATHML"><math> <mi>ε</mi> </math></EquationSource> </InlineEquation>-regularity criterion, we prove the parabolic fractal dimension of the possible interior singular set for the suitable weak solutions is bounded by <InlineEquation ID="IEq3"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="33_2025_2537_Article_IEq3.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="68" /> </InlineMediaObject> <EquationSource Format="TEX">\(\frac{7}{6}\approx 1.167\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mfrac> <mn>7</mn> <mn>6</mn> </mfrac> <mo>≈</mo> <mn>1.167</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Partial regularity and parabolic fractal dimension of singular points for the suitable weak solutions to 3D incompressible Navier–Stokes–Landau–Lifshitz system

  • 期刊论文

  • 发表日期：

    2025年7月3日

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  • Zhen Qiu,
  • Guangwu Wang

摘要

In this paper, we investigate the partial regularity of the suitable weak solution to three-dimensional incompressible Navier–Stokes–Landau–Lifshitz system and establish \(\varepsilon \) ε -regularity criteria. As an application of \(\varepsilon \) ε -regularity criterion, we prove the parabolic fractal dimension of the possible interior singular set for the suitable weak solutions is bounded by \(\frac{7}{6}\approx 1.167\) 7 6 ≈ 1.167 .