| Abstract: |
| In this talk I would like to present some results concerning a Navier-Stokes-Cahn-Hilliard model with singular
potential describing immiscible, viscous two-phase flows with matched densities, which is referred to as the
Model H, in three (and two) dimensional bounded domains.
I will first concentrate on some new results of local-in-time strong well-posedness for the nonlocal version
of the model H with singular potential. Namely, I will also discuss the validity of the instantaneous strict
separation property of the concentration variable from pure phases, by adapting the recent result for the
nonlocal Cahn-Hilliard equation in 3D by Poiatti (Anal. PDE, to appear).
I will then present the nonlocal-to-local convergence of strong solutions to the model H. This means that
the strong solutions to the nonlocal Model H converge to the strong solution to the local Model H as the
weight function in the nonlocal interaction kernel approaches the delta distribution. To this aim, I will show
some uniform bounds on the strong solutions to the nonlocal Model H, which are essential to prove the
nonlocal-to-local convergence results.
The novelty of this approach is that we are able to find precise convergence rates, in suitable norms, of the
strong solutions to nonlocal model H to the strong solution to local model H. |
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