Scholarlink

<p>A Cahn–Hilliard–Navier–Stokes system for two-phase flow on an evolving surface with non-matched densities is derived using methods from rational thermodynamics. For a Cahn–Hilliard energy with a singular (logarithmic) potential, short-time well-posedness of strong solutions together with a separation property is shown, under the assumption of <i>a priori </i>prescribed surface evolution. The problem is reformulated with the help of a pullback to the initial surface. Then a suitable linearization and a contraction mapping argument for the pullback system are used. In order to deal with the linearized system, it is necessary to show maximal <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(\displaystyle L^2\)</EquationSource> <EquationSource Format="MATHML"><math> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mn>2</mn> </msup> </mstyle> </math></EquationSource> </InlineEquation>-regularity for the surface Stokes operator in the case of variable viscosity and to obtain maximal <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(\displaystyle L^p\)</EquationSource> <EquationSource Format="MATHML"><math> <mstyle displaystyle="true" scriptlevel="0"> <msup> <mi>L</mi> <mi>p</mi> </msup> </mstyle> </math></EquationSource> </InlineEquation>-regularity for the linearized Cahn–Hilliard system.</p>

错误：搜索内容不能为空，请输入英文关键词
错误：关键词超出字数限制，请精简
高级检索

Diffuse interface model for two-phase flows on evolving surfaces with different densities: local well-posedness

  • 期刊论文

  • 出版模式：

    开放获取

  • 发表日期：

    2026年3月21日

查看全文
  • Helmut Abels,
  • Harald Garcke,
  • Andrea Poiatti

摘要

A Cahn–Hilliard–Navier–Stokes system for two-phase flow on an evolving surface with non-matched densities is derived using methods from rational thermodynamics. For a Cahn–Hilliard energy with a singular (logarithmic) potential, short-time well-posedness of strong solutions together with a separation property is shown, under the assumption of a priori prescribed surface evolution. The problem is reformulated with the help of a pullback to the initial surface. Then a suitable linearization and a contraction mapping argument for the pullback system are used. In order to deal with the linearized system, it is necessary to show maximal \(\displaystyle L^2\) L 2 -regularity for the surface Stokes operator in the case of variable viscosity and to obtain maximal \(\displaystyle L^p\) L p -regularity for the linearized Cahn–Hilliard system.