Two-phase incompressible flows with variable density: An energetic variational approach

Jie Jiang, Yinghua Li, Chun Liu

Research output: Contribution to journalArticlepeer-review

14 Scopus citations


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
Issue number6
StatePublished - 2017

All Science Journal Classification (ASJC) codes

  • Analysis
  • Discrete Mathematics and Combinatorics
  • Applied Mathematics


Dive into the research topics of 'Two-phase incompressible flows with variable density: An energetic variational approach'. Together they form a unique fingerprint.

Cite this