4 papers · 1 filter
Surface Stokes-Cahn-Hilliard System: Analysis and Structure-Preserving Discretization
Maxim Olshanskii, Mansur Shakipov
We study the surface Stokes-Cahn-Hilliard system governing tangential flow and phase separation in viscous fluid membranes. The equations are posed on a closed, stationary hy…
Existence of weak solutions of the surface Beris-Edwards model
Gonzalo A. Benavides, Ricardo H. Nochetto, Mansur Shakipov
We prove the existence of weak solutions to the surface Beris-Edwards model for nematic liquid crystals posed on a -dimensional () closed hypersurface of class $C…
Ferrofluids: Modeling and Approximation
Gonzalo A. Benavides, Ricardo H. Nochetto, Mansur Shakipov
Starting from Maxwell's and linear momentum balance equations, we derive a ferrofluid model using the generalized Onsager's principle. Guided by a discrete perturbation estimate, w…
-based Sobolev theory on closed manifolds of minimal regularity: Scalar Elliptic Equations
Gonzalo A. Benavides, Ricardo H. Nochetto, Mansur Shakipov
This paper and its follow-up arXiv:2508.11109 are concerned with the well-posedness and -based Sobolev regularity for appropriate weak formulations of a family of pro…