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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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
Keywords
- Diffuse interface model
- Nonhomogeneous Navier–Stokes equations
- Allen–Cahn equation
- Local strong solutions