Global well-posedness of the nonhomogeneous incompressible Navier-Stokes-Cahn-Hilliard system with Landau Potential

2024/09/18 by Rui, Nie, Li, Fang, Zhenhua, Guo · 1 citation
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2409.11775

Abstract

A diffuse-interface model that describes the dynamics of nonhomogeneous incompressible two-phase viscous flows is investigated in a bounded smooth domain in \mathbb R³. The dynamics of the state variables is described by the nonhomogeneous incompressible Navier-Stokes-Cahn-Hilliard system. We first give a blow-up criterion of local strong solution to the initial-boundary-value problem for the case of initial density away from zero. After establishing some key a priori with the help of the Landau Potential, we obtain the global existence and decay-in-time of strong solution, provided that the initial date ‖∇ u₀‖_L²(Ω)+‖∇ μ₀‖_L²(Ω)+ρ₀ is suitably small.

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