Existence of weak solutions for a non-classical sharp interface model for a two-phase flow of viscous, incompressible fluids

Abstract

We introduce a new sharp interface model for the flow of two immiscible, viscous, incompressible fluids. In contrast to classical models for two-phase flows we prescribe an evolution law for the interfaces that takes diffusional effects into account. This leads to a coupled system of Navier-Stokes and Mullins-Sekerka type parts that coincides with the asymptotic limit of a diffuse interface model. We prove the long-time existence of weak solutions, which is an open problem for the classical two-phase model. We show that the phase interfaces have in almost all points a generalized mean curvature.

26 pages

References in corpus (1)

• Two-phase binary fluids and immiscible fluids described by an order parameter

Cited by in corpus (8)

• Existence of Weak Solutions for a Diffuse Interface Model for Two-Phase Flows of Incompressible Fluids with Different Densities
• Degenerate nonlocal Cahn-Hilliard equations: well-posedness, regularity and local asymptotics
• A Hele-Shaw-Cahn-Hilliard model for incompressible two-phase flows with different densities
• Local asymptotics for nonlocal convective Cahn-Hilliard equations with W^{1,1} kernel and singular potential
• Weak-strong uniqueness for the Navier-Stokes equation for two fluids with surface tension
• On a Navier-Stokes-Allen-Cahn model with inertial effects
• Thermodynamically Consistent Diffuse Interface Models for Incompressible Two-Phase Flows with Different Densities
• Two-phase flow problem coupled with mean curvature flow