Premium
Weak solutions for a diffuse interface model for two‐phase flows of incompressible fluids with different densities and nonlocal free energies
Author(s) -
Abels Helmut,
Terasawa Yutaka
Publication year - 2020
Publication title -
mathematical methods in the applied sciences
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.719
H-Index - 65
eISSN - 1099-1476
pISSN - 0170-4214
DOI - 10.1002/mma.6111
Subject(s) - mathematics , bounded function , compressibility , discretization , newtonian fluid , interface model , mathematical analysis , norm (philosophy) , incompressible flow , domain (mathematical analysis) , space (punctuation) , weak solution , flow (mathematics) , mechanics , physics , geometry , linguistics , philosophy , human–computer interaction , computer science , political science , law
We consider a diffuse interface model for the flow of two viscous incompressible Newtonian fluids with different densities in a bounded domain in two and three space dimensions and prove existence of weak solutions for it. In contrast to earlier contributions, we study a model with a singular nonlocal free energy, which controls the H α /2 ‐norm of the volume fraction. We show existence of weak solutions for large times with the aid of an implicit time discretization.