A finite element continuous data assimilation framework for a Navier–Stokes–Cahn–Hilliard system
arXiv:2603.08765v1 Announce Type: new Abstract: This paper studies a coupled two-dimensional Navier–Stokes–Cahn–Hilliard phase-field model augmented by a transported auxiliary field, and develops a continuous data assimilation (CDA) framework for recovering its trajectories from coarse-in-space observations. We formulate a nudging-based CDA system for the coupled NSCH–auxiliary-field model, in which coarse measurements are incorporated through a general linear observation operator. The observation mechanism is described abstractly by an interpolant satisfying an $H^{2}$-type approximation property, which is compatible with coarse spatial […]