Global existence of weak solutions for a nonlocal model for two-phase flows of incompressible fluids with unmatched densities
- Frigeri, Sergio Pietro
2010 Mathematics Subject Classification
- 76T99 35Q30 35Q35 76D03 76D03 76D05 76D27
- Diffuse interface model, Incompressible viscous binary fluids, Navier--Stokes system, nonlocal Cahn--Hilliard equation
We consider a diffuse interface model for an incompressible isothermal mixture of two viscous Newtonian fluids with different densities in a bounded domain in two or three space dimensions. The model is the nonlocal version of the one recently derived by Abels, Garcke and Grün and consists of a Navier-Stokes type system coupled with a convective nonlocal Cahn-Hilliard equation. The density of the mixture depends on an order parameter. For this nonlocal system we prove existence of global dissipative weak solutions for the case of singular double-well potentials and non degenerate mobilities. To this goal we devise an approach which is completely independent of the one employed by Abels, Depner and Garcke to establish existence of weak solutions for the local Abels et al. model.
- Math. Models Methods Appl. Sci., 26 (2016), pp. 1957--1993.