Low Mach Number Limit of a Diffuse Interface Model for Two-Phase Flows of Compressible Viscous Fluids

Abstract

In this paper, we consider a singular limit problem for a diffuse interface model for two immiscible compressible viscous fluids. Via a relative entropy method, we obtain a convergence result for the low Mach number limit to a corresponding system for incompressible fluids in the case of well-prepared initial data and same densities in the limit.

arXiv comment15 pages

References in corpus (5)

• Two-phase binary fluids and immiscible fluids described by an order parameter
• Relative entropies, suitable weak solutions, and weak strong uniqueness for the compressible Navier-Stokes system
• Weak-strong uniqueness for the isentropic compressible Navier-Stokes system
• Weak-strong uniqueness property for the full Navier-Stokes-Fourier system
• Weak solutions to the stationary Cahn-Hillard/Navier-Stokes equations for compressible fluids