A diffuse interface model for two-phase incompressible flows with\n nonlocal interactions and nonconstant mobility

2013/03/26 by Sergio Frigeri, Frigeri, Sergio, Maurizio Grasselli +3 · 2 citations
Materials Science · Engineering · #Solidification and crystal growth phenomena #Fluid Dynamics and Thin Films

paper · pdf · doi:10.48550/arxiv.1303.6446

Abstract

We consider a diffuse interface model for incompressible isothermal mixtures\nof two immiscible fluids with matched constant densities. This model consists\nof the Navier-Stokes system coupled with a convective nonlocal Cahn-Hilliard\nequation with non-constant mobility. We first prove the existence of a global\nweak solution in the case of non-degenerate mobilities and regular potentials\nof polynomial growth. Then we extend the result to degenerate mobilities and\nsingular (e.g. logarithmic) potentials. In the latter case we also establish\nthe existence of the global attractor in dimension two. Using a similar\ntechnique, we show that there is a global attractor for the convective nonlocal\nCahn-Hilliard equation with degenerate mobility and singular potential in\ndimension three.\n

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• Two phase micropolar fluid flow with nonlocal energies: Existence theory, nonpolar limits and nonlocal-to-local convergence
• Optimal error estimates of the diffuse domain method for semilinear parabolic equations

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