M. Shakipov

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20242026

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math.AP2026

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 $C^{2}$ hy…

math.AP2026

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 $d$ -dimensional ( $d \in {2, 3}$ ) closed hypersurface of class $C…

math.AP2026

$L^{p}$ -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 $L^{p}$ -based Sobolev regularity for appropriate weak formulations of a family of pro…

Surface Stokes-Cahn-Hilliard System: Analysis and Structure-Preserving Discretization

Existence of weak solutions of the surface Beris-Edwards model

Lp-based Sobolev theory on closed manifolds of minimal regularity: Scalar Elliptic Equations

$L^{p}$ -based Sobolev theory on closed manifolds of minimal regularity: Scalar Elliptic Equations