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<p>In this paper, we present some new regularity criteria for suitable weak solutions to the 3D co-rotational Beris-Edwards system. First, we prove that suitable weak solutions are regular if the scaled <i>L</i><sup><i>p</i>;<i>q</i></sup>-norm of the velocity field or gradient of velocity is small with <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\({2\over p}+{3\over q}=2,1 &lt; p \leq \infty\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mrow> <mfrac> <mn>2</mn> <mi>p</mi> </mfrac> </mrow> <mo>+</mo> <mrow> <mfrac> <mn>3</mn> <mi>q</mi> </mfrac> </mrow> <mo>=</mo> <mn>2</mn> <mo>,</mo> <mn>1</mn> <mo>&lt;</mo> <mi>p</mi> <mo>≤</mo> <mi mathvariant="normal">∞</mi> </math></EquationSource> </InlineEquation>. Next, we give <i>ε</i>-regularity criteria in terms of velocity field <b>u</b> and director field <b>Q</b> in Lorentz spaces, which extends the results obtained by Wang et al (J. Evol. Equ. 21: 1627–1650, 2021) for Navier-Stokes equations.</p>

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Local Regularity Criteria for the 3D Co-rotational Beris-Edwards System in Lorentz Spaces

  • 期刊论文

  • 发表日期：

    2026年1月2日

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  • Zhong-bao Zuo

摘要

In this paper, we present some new regularity criteria for suitable weak solutions to the 3D co-rotational Beris-Edwards system. First, we prove that suitable weak solutions are regular if the scaled Lp;q-norm of the velocity field or gradient of velocity is small with \({2\over p}+{3\over q}=2,1 < p \leq \infty\) 2 p + 3 q = 2 , 1 < p ≤ ∞ . Next, we give ε-regularity criteria in terms of velocity field u and director field Q in Lorentz spaces, which extends the results obtained by Wang et al (J. Evol. Equ. 21: 1627–1650, 2021) for Navier-Stokes equations.