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<p>We investigate regularity criteria for weak solutions to the three-dimensional non-Newtonian MHD-type system for <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({11\over{5}}\leqslant q&lt;{5\over{2}}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mfrac> <mn>11</mn> <mrow> <mn>5</mn> </mrow> </mfrac> </mrow> <mo>⩽</mo> <mi>q</mi> <mo>&lt;</mo> <mrow> <mfrac> <mn>5</mn> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math></EquationSource> </InlineEquation> under a sufficient condition involving only the magnetic field. In addition, weak-strong uniqueness in ℝ<sup>3</sup> is established for <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(q\geqslant{5\over{2}}\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mi>q</mi> <mo>⩾</mo> <mrow> <mfrac> <mn>5</mn> <mrow> <mn>2</mn> </mrow> </mfrac> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Regularity criteria for weak solutions to 3D non-Newtonian fluid equations of MHD type

  • 期刊论文

  • 发表日期：

    2026年5月25日

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  • Jae-Myoung Kim

摘要

We investigate regularity criteria for weak solutions to the three-dimensional non-Newtonian MHD-type system for \({11\over{5}}\leqslant q<{5\over{2}}\) 11 5 ⩽ q < 5 2 under a sufficient condition involving only the magnetic field. In addition, weak-strong uniqueness in ℝ3 is established for \(q\geqslant{5\over{2}}\) q ⩾ 5 2 .