5 papers
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: Vector-valued problems
Gonzalo A. Benavides, Ricardo H. Nochetto, Mansur Shakipov
This paper is the second part of a two-paper series, initiated in arXiv:2603.02163 for scalar PDEs on hypersurfaces, and is concerned with the well-posedness and -bas…
-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…
Surface Stokes Without Inf-Sup Condition
Ricardo H. Nochetto, Mansur Shakipov
For a -dimensional hypersurface of class without boundary, we reformulate the surface Stokes equations as a nonsymmetric indefinite elliptic problem governed by two Laplac…