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<p>In this paper we study the global regularity problem for the 2D micropolar Rayleigh-Bénard convection system with velocity logarithmic supercritical dissipation and temperature zero diffusion. By introducing a combined quantity and using the technique of Littlewood-Paley decomposition, we establish the global regularity result of strong solutions to this system in the Sobolev space <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2025_2447_Article_IEq1.gif" Format="GIF" Height="20" Rendition="HTML" Resolution="72" Type="Linedraw" Width="52" /> </InlineMediaObject> <EquationSource Format="TEX">\(H^s(\mathbb {R}^2)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <msup> <mi>H</mi> <mi>s</mi> </msup> <mrow> <mo stretchy="false">(</mo> <msup> <mrow> <mi mathvariant="double-struck">R</mi> </mrow> <mn>2</mn> </msup> <mo stretchy="false">)</mo> </mrow> </mrow> </math></EquationSource> </InlineEquation> for <InlineEquation ID="IEq2"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="25_2025_2447_Article_IEq2.gif" Format="GIF" Height="15" Rendition="HTML" Resolution="72" Type="Linedraw" Width="41" /> </InlineMediaObject> <EquationSource Format="TEX">\(s\ge 2\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>s</mi> <mo>≥</mo> <mn>2</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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Global Regularity for the 2D Micropolar Rayleigh-Bénard Convection System with Velocity Logarithmic Supercritical Dissipation and Temperature Zero Diffusion

  • 期刊论文

  • 发表日期：

    2025年6月9日

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  • Xin Chen,
  • Baoquan Yuan

摘要

In this paper we study the global regularity problem for the 2D micropolar Rayleigh-Bénard convection system with velocity logarithmic supercritical dissipation and temperature zero diffusion. By introducing a combined quantity and using the technique of Littlewood-Paley decomposition, we establish the global regularity result of strong solutions to this system in the Sobolev space \(H^s(\mathbb {R}^2)\) H s ( R 2 ) for \(s\ge 2\) s ≥ 2 .