Published Paper

Inserted: 24 nov 2025
Last Updated: 30 sep 2026

Journal: Math. Models Methods Appl. Sci.
Year: 2025
Doi: 10.1142/S0218202526500466

Abstract:

We propose a thermodynamically consistent phase-field model for the flow of a mixture of two different viscous incompressible fluids of equal density in a bounded domain. We prove the well-posedness of local-in-time strong solutions by means of maximal regularity and contraction mapping arguments. We introduce a suitable entropic weak formulation of the problem, replacing the heat equation by the total energy inequality and an entropy production inequality, and we rigorously prove global-in-time existence of such weak solutions, developing a novel approximation scheme. We also show that an entropic weak solution to this non-isothermal phase-field model converges to a distributional (or $BV$) solution to a non-isothermal Navier--Stokesmean curvature flow, under an energy convergence assumption.