Scholarlink

<p>In this paper, we investigate a nonlinear system describing nonhomogeneous and incompressible fluids with viscoelastic properties. The system integrates the generalized Kelvin–Voigt equations for nonhomogeneous and incompressible fluid flows, with a convective local Cahn–Hilliard equation for the order (phase) parameter. Our analysis focuses on case in which the initial density is nonzero and the potential is either smooth with arbitrary polynomial growth or singular (e.g., logarithmic type). Additionally, we consider the momentum equation perturbed by an extra term, which represents either a source or a sink within the system, depending on its sign. For regular potentials, we demonstrate the global existence of weak solutions in the presence of a sink and the local existence of weak solutions in the presence of a source. Building upon these results and using an approximation technique that replaces the singular potential with a sequence of regular potential, we further prove the global existence of weak solutions for singular potentials in a presence of a sink.</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

Weak solutions to the generalized nonhomogeneous incompressible Kelvin–Voigt–Cahn–Hilliard system

  • 期刊论文

  • 发表日期：

    2025年6月25日

查看全文
  • A. Ndongmo Ngana,
  • T. Tachim Medjo,
  • P. M. Tchepmo Djomegni

摘要

In this paper, we investigate a nonlinear system describing nonhomogeneous and incompressible fluids with viscoelastic properties. The system integrates the generalized Kelvin–Voigt equations for nonhomogeneous and incompressible fluid flows, with a convective local Cahn–Hilliard equation for the order (phase) parameter. Our analysis focuses on case in which the initial density is nonzero and the potential is either smooth with arbitrary polynomial growth or singular (e.g., logarithmic type). Additionally, we consider the momentum equation perturbed by an extra term, which represents either a source or a sink within the system, depending on its sign. For regular potentials, we demonstrate the global existence of weak solutions in the presence of a sink and the local existence of weak solutions in the presence of a source. Building upon these results and using an approximation technique that replaces the singular potential with a sequence of regular potential, we further prove the global existence of weak solutions for singular potentials in a presence of a sink.