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<p>In this paper, we consider the Cauchy problem to a 3D hydrodynamic phase-field model describes the deformation of functionalized membranes in an incompressible viscous fluid, or the phase separation process of incompressible viscous two-phase flows with an amphiphilic structure. This model consists of the incompressible Navier-Stokes equations coupled with a sixth-order convective Cahn-Hilliard equation driven by the functionalized Cahn-Hilliard free energy. The local well-posedness, small initial data global well-posedness of strong solution as well as the time decay estimates in higher order Sobolev spaces are obtained by introducing a perturbation form with respect to <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="40840_2025_1958_Article_IEq1.gif" Format="GIF" Height="19" Rendition="HTML" Resolution="72" Type="Linedraw" Width="70" /> </InlineMediaObject> <EquationSource Format="TEX">\((u,\phi -1)\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mo stretchy="false">(</mo> <mi>u</mi> <mo>,</mo> <mi>ϕ</mi> <mo>-</mo> <mn>1</mn> <mo stretchy="false">)</mo> </mrow> </math></EquationSource> </InlineEquation>.</p>

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On strong solution to a hydrodynamic phase-field model for functionalized membrane-fluid interaction

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • Yayi Liu,
  • Ning Duan,
  • Ping Fang,
  • Xiaopeng Zhao

摘要

In this paper, we consider the Cauchy problem to a 3D hydrodynamic phase-field model describes the deformation of functionalized membranes in an incompressible viscous fluid, or the phase separation process of incompressible viscous two-phase flows with an amphiphilic structure. This model consists of the incompressible Navier-Stokes equations coupled with a sixth-order convective Cahn-Hilliard equation driven by the functionalized Cahn-Hilliard free energy. The local well-posedness, small initial data global well-posedness of strong solution as well as the time decay estimates in higher order Sobolev spaces are obtained by introducing a perturbation form with respect to \((u,\phi -1)\) ( u , ϕ - 1 ) .