Two-phase incompressible flows with variable density

An energetic variational approach

Jie Jiang, Yinghua Li, Chun Liu

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper, we study a diffuse-interface model for two-phase incompressible flows with different densities. First, we present a derivation of the model using an energetic variational approach. Our model allows large density ratio between the two phases and moreover, it is thermodynamically consistent and admits a dissipative energy law. Under suitable assumptions on the average density function, we establish the global existence of a weak solution in the 3D case as well as the global well-posedness of strong solutions in the 2D case to an initial-boundary problem for the resulting Allen-Cahn-Navier-Stokes system. Furthermore, we investigate the longtime behavior of the 2D strong solutions. In particular, we obtain existence of a maximal compact attractor and prove that the solution will converge to an equilibrium as time goes to infinity.

Original languageEnglish (US)
Pages (from-to)3243-3284
Number of pages42
JournalDiscrete and Continuous Dynamical Systems- Series A
Volume37
Issue number6
DOIs
StatePublished - Jan 1 2017

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Incompressible flow
Variational Approach
Two-phase Flow
Incompressible Flow
Strong Solution
Diffuse Interface
Global Well-posedness
Navier-Stokes System
Long-time Behavior
Boundary Problem
Density Function
Global Existence
Probability density function
Weak Solution
Attractor
Infinity
Model
Converge
Energy

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics

Cite this

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Two-phase incompressible flows with variable density : An energetic variational approach. / Jiang, Jie; Li, Yinghua; Liu, Chun.

In: Discrete and Continuous Dynamical Systems- Series A, Vol. 37, No. 6, 01.01.2017, p. 3243-3284.

Research output: Contribution to journalArticle

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