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<p>We investigate a system of partial differential equations that models the motion of an incompressible double-diffusion convection fluid. The additional stress tensor is generated by a potential with <i>p</i>-structure. In a three-dimensional periodic setting and <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="10492_2025_6824_Article_IEq1.gif" Format="GIF" Height="22" Rendition="HTML" Resolution="72" Type="Linedraw" Width="66" /> </InlineMediaObject> <EquationSource Format="TEX">\(p \in [{{5} \over {3}},2)\)</EquationSource> <EquationSource Format="MATHML"><math display="block"> <mi>p</mi> <mo>∈</mo> <mo stretchy="false">[</mo> <mrow> <mfrac> <mrow> <mn>5</mn> </mrow> <mrow> <mn>3</mn> </mrow> </mfrac> </mrow> <mo>,</mo> <mn>2</mn> <mo stretchy="false">)</mo> </math></EquationSource> </InlineEquation>, we employ a regularized approximation scheme in conjunction with the Galerkin method to establish the existence of regular solutions, provided that the forcing term is properly small. Furthermore, we demonstrate the existence of periodic regular solutions with period <i>T</i> when the external force exhibits periodicity in time with the same period <i>T</i>.</p>

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Existence of regular time-periodic solutions for a class of non-Newtonian double-diffusive convection system

  • 期刊论文

  • 发表日期：

    2025年6月9日

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  • Qiong Wu,
  • Changjia Wang

摘要

We investigate a system of partial differential equations that models the motion of an incompressible double-diffusion convection fluid. The additional stress tensor is generated by a potential with p-structure. In a three-dimensional periodic setting and \(p \in [{{5} \over {3}},2)\) p ∈ [ 5 3 , 2 ) , we employ a regularized approximation scheme in conjunction with the Galerkin method to establish the existence of regular solutions, provided that the forcing term is properly small. Furthermore, we demonstrate the existence of periodic regular solutions with period T when the external force exhibits periodicity in time with the same period T.