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Strong solutions for an incompressible Navier–Stokes/Allen–Cahn system with different densities

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Abstract

In this paper, we investigate a coupled Navier–Stokes/Allen–Cahn system describing a diffuse interface model for two-phase flow of viscous incompressible fluids with different densities in a bounded domain \(\Omega \subset \mathbb R^N\)(\(N=2,3\)). We prove the existence and uniqueness of local strong solutions to the initial boundary value problem when the initial density function \(\rho _0\) has a positive lower bound.

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Authors and Affiliations

  1. School of Mathematical Sciences, South China Normal University, Guangzhou, 510631, China

    Yinghua Li & Mingxia Huang

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  1. Yinghua Li
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  2. Mingxia Huang
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Correspondence to Yinghua Li.

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Li, Y., Huang, M. Strong solutions for an incompressible Navier–Stokes/Allen–Cahn system with different densities. Z. Angew. Math. Phys. 69, 68 (2018). https://doi.org/10.1007/s00033-018-0967-0

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  • DOI: https://doi.org/10.1007/s00033-018-0967-0

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