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<p>We study the global well-posedness of Doi–Saintillan–Shelley (DSS) model for passive rod-like particle suspensions in <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\mathbb {R}^2\)</EquationSource> <EquationSource Format="MATHML"><math> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>2</mn> </msup> </math></EquationSource> </InlineEquation>. We first construct the local existence of smooth solution to type-I DSS model without the translational diffusion and present a blow-up criterion. From which we deteriorate regularity estimate for transport equation, and then, we prove the global existence of smooth solution. Next, by introducing a bounded operator on <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\mathbb {S}\)</EquationSource> <EquationSource Format="MATHML"><math> <mi mathvariant="double-struck">S</mi> </math></EquationSource> </InlineEquation>, we prove the global existence of smooth solution to type-II DSS model.</p>

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Global existence of smooth solution to Doi-type model without translational diffusion

  • 期刊论文

  • 发表日期：

    2026年7月6日

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  • Zhong Tan,
  • Jianfeng Zhou

摘要

We study the global well-posedness of Doi–Saintillan–Shelley (DSS) model for passive rod-like particle suspensions in \(\mathbb {R}^2\) R 2 . We first construct the local existence of smooth solution to type-I DSS model without the translational diffusion and present a blow-up criterion. From which we deteriorate regularity estimate for transport equation, and then, we prove the global existence of smooth solution. Next, by introducing a bounded operator on \(\mathbb {S}\) S , we prove the global existence of smooth solution to type-II DSS model.