Two phase micropolar fluid flow with unmatched densities modeled by Navier--Stokes--Cahn--Hilliard systems: Local strong well-posedness and consistency estimates

2025/05/29 by Chan, Kin Shing, Lam, Kei Fong · 1 citation
#35A01 #35D35 #35K35 #35Q35 #76D03 #76D45 #76T06 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2505.23235

Abstract

We study a thermodynamically consistent phase field model for binary mixtures of micropolar fluids, i.e., fluids exhibiting internal rotations. Furnishing with classical no-slip, no-spin and no-flux boundary conditions, in a smooth and bounded three-dimensional domain, we establish the well-posedness of local-in-time strong solutions. Since the model studied is a generalization of the earlier model introduced by Abels, Garcke and Grün for binary Newtonian fluids with unmatched densities, we provide a consistency result between the corresponding strong solutions to both models in terms of a parameter associated to the micro-rotation viscosity.

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• Two phase micropolar fluid flow with nonlocal energies: Existence theory, nonpolar limits and nonlocal-to-local convergence

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